I'd say it's not so much that he hasn't won, its that he's never been really close. They've been perennial also runs in the league and Europe for basically a decade.
This.
The FA Cups are great to win. Gives the fans a moment of pride, we see our team lift a trophy at Wembley and it's one of the more storied competitions in Europe. Beating a crosstown rival is icing on the cake.
If we were Everton or West Ham, it would be a great story.
But we've seen this movie before. When we won in 2014 and 2015, title challenges were supposed to be coming. They didn't. And like usual, we were laughed out of the CL.
Truly the last time we were in contention in the League was maybe 2014, finishing seven points back, but we were throttled badly in losses to Man City, Liverpool, Chelsea and Everton. So while we looked close on paper, it's safe to say we were never truly in it. Before that? 2008.
I firmly believe Wenger will be staying, solely based off this Cup win, but I can't see how part 3 is going to be any different than the first two post-Cup win installments. If this season was any indication, it's going to be even worse.
Tricky part is, if there's no one of quality to replace him, we're better off with him staying but have him announce his he's leaving at the end of the contract.