I think it's fair to say Arsene's ability to buy bargain players has died up. Gone are the days of Henry/Viera/Van Percy coming in as mediocre players only to be indispensable a season later.
I think if you look at some of the more recent meteoric rises, they all seems to come from lesser leagues or clubs, BVB/Juventus/Atlético Madrid/Porto, and to some extent Liverpool/Spurs (Bale/Suarez/Sterling/Coutinho/Kane).
I think signing a player with potential is only part of the issue, the key is playing, developing and nurturing them. With teams like BVB/Juventus/Atlético Madrid/Porto they are either in easier leagues where a player doesn't have to be the finished article to excel, or financially constrained to not be able to purchase the finished article. With Spurs and Liverpool they fall into the later category so are forced to give youth players a chance.
Take Kevin De Bruyne as an example, an obvious talent purchased by Chelsea, but not played because he wasn't quite finished (perhaps only in reputation rather than ability). Sold to play in a lesser league where he excelled, and then purchased for 50 million where his stature and starting place are then almost granted.
These days I think Arsene is stuck in a position where he has the money to spend, but ideally want's to return to his roots of nurturing young players. However the fans and board aren't willing to gamble on youth, in favor of signing 40/50 million finished articles.
A few million on an analytic company isn't going to break the bank, and may be more valuable in opposition analysis than finding the next rough diamond.