Deciding against signing Fabregas cannot be because Arsene Wenger is unaware of the world-class quality of the player. After all, he worked with Fabregas for many years at Arsenal.
To say that he won't sign Fabregas because that would create an overload of creative players at the club is to display shortsightedness, lack of guile and lack of imagination. But more on this in the following.
One very persuasive reason why Arsenal should re-sign Fabregas is because he is the best quick-switch midfielder in all of Europe.
What is quick-switch?
A quick-switch player is one who advances play so quickly that the opponent is taken by surprise, having had no time to reorganize its defensive shape. This player has uncanny vision and sees a pass, often long-range, where others don't.
Such a player enables the team to create chances seemingly out of nothing. He helps a team to turn over a large percentage of goals and chances. In the case of Fabregas, this helps explain why Arsenal (even in their barren seasons) used to create and score a great number of goals even as they were defensively fragile.
Diego Forlan (to give an example) tends to do this for Uruguay.
The Uruguay national team advanced far in the 2010 World Cup largely due to Forlan's influence, who often executed pinpoint passes that advanced his team's attack very quickly.
Andrea Pirlo would be another example but he now operates very deep and is not as effective in terms of quickly advancing an attacking play.
Now the reader may wonder whether this isn't exactly what Mesut Ozil brings to Arsenal. Does he not possess the same quality and vision?
It may be.
But to me they are two different players (to state the obvious). To essentialize and oversimplify, it seems to me that Ozil is dominantly what I'd call a "floor-passer": that is, his passes are mostly low, on-the-ground passes (defense-splitting, granted).
Fabregas, meanwhile, seems to be dominantly an over-the-top passer—he tends to loop the ball over the last defensive line of the opposition.
But like I said, this may be an oversimplification. It does not mean that Ozil never passes over the top or that Fabregas never passes on the floor.
In terms of quick-switch itself, I'd say the person who does this for the current Arsenal team isn't even Ozil. It is Tomas Rosicky. Whereas Ozil is bound to find the final pass, he is not as adept at switching play so quickly from defense to attack as Rosicky is.
On this point one might say Ozil is a finisher (in terms of completing an attacking move) while Rosicky is an initiator. If the reader grasps this distinction, then he or she can discern the contrast between Ozil and Fabregas which I have attempted to draw in the above.
Thus, Fabregas is a very potent initiator of an attack in a way that Ozil is not. Furthermore, Fabregas is a better finisher than Ozil. Moreover, Fabregas can do what Ozil does so well.
In essence, adding Fabregas to the squad will not be a multiplication of essences but an addition of a complementary quality, a diversification that'll enable Arsenal to be more prolific and fertile in its attack.
Moreover, on the point of being a potent initiator (quick-switch, that is), the fact that Rosicky may not have very many years left at Arsenal is all the more reason why Arsenal should sign Fabregas specifically for this role. If Rosicky can play with Ozil, why not Fabregas? Or if Rosicky is at Arsenal in spite of Ozil, why not Fabregas?
In any case, signing Fabregas will never be a loss or a mistake for Arsenal. It can only be an addition, a strengthening of the squad. This is why I believe it is quite foolish to let Chelsea have him.