I'd like to start off my rebuttal by saying that I highly respect outie's football knowledge, and I only jokingly said I wanted to debate him because I knew he'd provide a thoughtful response and be willing to go back and forth, point and counterpoint. In his post, which I will address in detail, he said he had to provide two arguments against Götze, one for him as the AM and one as the wide forward. I don't see that yet, so we'll cross that bridge when we get there I suppose.
In opening, I'd like to state something that should be obvious but may get overlooked. While its one thing to have an opinion on a player, to feel strongly about him, and to support him ending up at Arsenal, none of us really know for sure. The reason for this is threefold. Every team is set up differently, especially at the top level. Teams have different ways of doing things, they employ different types of training regiments, different systems, different everything. For some players, the fit is natural, for other players, the fit isn't natural and things don't work. As good as a player is, for any number of reasons it can go all wrong. That doesn't necessarily mean you were wrong about the player, it just means it is impossible to really know what will happen until it does.
Now that I've gotten that out of the way. I tend to look at football players on a 2-8 scale, which then follows a bell curve distribution. Most players fall in the middle, a 5, in terms of their capability on the pitch. You have 3 standard deviations from the mean. A 6 is an above average talent, a 7 is a well above average talent, and an 8 is the absolute best of the best on the planet. Conversely, a 4 is below average, a 3 is well below average, and a 2 is one of the worst players ever. At the highest levels, the Premier League and the top tiers of the other big European leagues, many players fall in the middle, like the bell curve illustrates.

For me, Mario Götze is either a 7 or an 8. At 19.5 years of age, he's one of the top talents in Europe.
The thing that separates good players from the best players, in my opinion, is something innate, something that you can't measure with sprint times, or bench press reps, or any other physical measure. The human brain processes information differently in different people. Some people have heightened spatial memory ability...which helps them process their surroundings. Some people have faster reactions than others. These things can be trained to some degree, but not to the same degree as physical, exterior traits. Take a player like Cesc. No matter where he was on the pitch, he always seemed to have a keen sense of awareness. From my time watching him, I feel Götze is cut from the same cloth.
My comments below are based on watching him play last season. I'd guess that I've probably seen him play 10-15 full games, and then a bunch of highlight packages. I'm no scout, I'm not saying my opinion is more valid than anyone else's, these are just my thoughts.
I see 3 reasons why he would be a perfect fit for Arsenal. First and foremost, his technical ability suits the team and our style of play. His close control, two footedness, and vision with the ball are all exceptional given his age. He played the entire 2010-2011 season at age 18, and he became the fulcrum of the Dortmund attack. Now I'm not going to argue the Bundesliga is on the same level as the Premier League, but its one of the 4 best leagues in the world, and to become the centerpiece of attack for a title winning team at 18 puts you in special company. In 2005-2006, when Cesc was 18, he made 50 total appearances, scoring 5 goals and providing 7 assists. Last season, Götze made 41 appearances, scoring 8 goals and providing 12 assists.
The second attribute that is going to make him one of the world's best is his anticipation and vision. I've seen games where he's played deeper, and every time he received the ball he'd picked his head up a split second earlier to see where the ball was supposed to go next. This is the same thing that made Cesc so good. He had already played out the next move in his head and executing the pass or dribble was just second nature. Vision and awareness are arguably the two most important traits a footballer can have, and in a lot of cases, based on what I've read, you can argue that it is innate.
The third trait that will make him a success at Arsenal is his adaptability. As I mentioned above, I've seen him deployed deeper in the midfield, as well as playing the AM role outie mentioned, and also playing as a wide forward. Despite his tender age and lack of experience, Klopp has been confident enough in him to use him all over the park. For a team like Arsenal, positioning is very fluid. The 6 non-defender outfield players for Arsenal interchange all over the pitch. Sometimes Song finds himself ahead of Arteta and Ramsey, sometimes its Arteta that is the deepest midfielder and sometimes he is closest to goal. For the three forwards, Walcott and Gervinho often switch flanks, both guys like cutting in to the center, and van Persie is notorious for dropping really deep to pick up the ball and bring himself in to the game. In this sense, Götze would not find himself out of place, as he'd be able to quickly adapt to whatever role was given to him.
Götze is just 5'9, but he possesses excellent pace. He can beat the fullback down the flank, and he's capable of skipping through the center of the pitch with the ball at his feet. He doesn't have the defensive nous to be a holding midfielder, but I would argue that with experience, he would be no worse than Arteta defensively playing in central midfield. From a size angle, he is very similar to Fabregas, and before pushing forward to the #10ish role, Cesc operated as a CM, often dropping very deep to pick up the ball.
I've seen him compared to Nasri and Hleb, though I don't think either comparison is really fair. I probably watched a bit less of Nasri when he was at Marseille. I thought he was a great prospect, but Götze has much more pace, his vision is superior, and his weaker foot was more developed at the same age. Hleb is a different type of player as well, with Götze again displaying much more pace and willingness to run past his man. Again, look at any of these players and examine what they did at age 18 and then compare it what Götze did at age 18.
The big issue outie seems to have is where Götze fits in to this team. I think I've kind of outlined where he would fit in, but I'm going to address his comments point by point
It is worth establishing that I believe Gotze to have all the right tools in order to occupy the much coveted AM position. The issue I have is with the position itself, as opposed to the quality of the German. The problem with the pyramid shaped midfield is that it encompasses a specialist offensive role. There is nothing inherently wrong with that, but there are various ramifications of implementing the AM role within the formation. The most obvious point is that the incumbent becomes highly integral to the performance of the team, given that he is essentially central to everything that occurs in an offensive sense. Again, there is nothing wrong with building the team around a player, but there are several problems that arise.
In a sense, I agree. I assume by "pyramid" you are referring to two deeper midfielders and then the AM in front of the two. I don't think this type of setup is necessarily good or bad, I suppose it depends on the competition. And I think again, that is a plus for Götze. He does not have to play centrally in the AM role, and could realistically operate in any of the 6 spots in front of the back 4. The current team, as it is, is built around RvP. We don't have a viable backup option to van Persie, as has been illustrated quite clearly this season. As I mentioned above in my outline, Arsenal's positioning is very fluid when they collect the ball, with any of the 6 non-defenders willing to move up and move in to attacking positions. When talking formations, I think you're only looking at where players stand when the game starts and the expectations you have of players in terms of attacking/defending responsibilities.
I agree with your second long paragraph and conclusion. Building the team around one player, tailoring the entire formation and style of play around that player, is dangerous. But Arsenal haven't done that at any point. The problem now is a lack of depth in the squad. If RvP takes a knock, we're well and truly ****** because we don't have another central striker. Götze isn't the same type of attacker as RvP, but he's capable of playing wide forward and in the midfield, and that offers you the ability to use him in a number of different roles. Neither of our current wide forwards, Gervinho or Walcott, have proven themselves to be undroppable, dead certain starters week in and week out. Both players show glimpses of being great players, but both are flawed and show their weaknesses as well.
In summary. Götze is a special talent. Its possible that he is a generational talent. Right now, our team is set up one way under Wenger, using a 4-3-3 of some sort. But this is a recent change, as we played 4-4-2 or 4-5-1 forever before making this change. In a year or two, a player of Götze's caliber may well be completely unattainable. If he moves to Real Madrid or Barcelona, he's only leaving if his career goes off track, and at that point you might not want a reclamation project. We don't know how long Wenger will stay. We don't know what he will do with the formation or tactics going forward.
What I do know is, talent, special talent, is what propels you from good team to great team. For a team like Arsenal, where teams have the mindset to play very deep and try to form a defensive wall, you need creative match winners. You need people who can run at a defender, switch the ball to the other foot and either pick out a pass or take a quick shot. You need players with superior vision and awareness, willing to see the smallest glimmer of open space and make the perfect pass. Götze has that ability.
I understand the concerns outie has. But I don't feel we would need to change anything in terms of the setup of the team. Götze plugs in at either wide forward, and he can play in the midfield 3 as well, especially against a non-Barca/Man City type team. A player of his ability fits in to any team.
Time's yours.
(sorry for the lack of multimedia bells and whistles, I have a bunch of stuff to do and have to take off)