Sounds a bit like what Wenger had to face when he first arrived at the club. Similar narrative.
I'd say that our next manager has a tougher task. Wenger inherited a very good solid team which he moulded into a modern force. Our current team has defensive and midfielding problems which the team of yesteryear didn't have. I'd take it further and throw in our attack. We may have some fine attacking players, but we still haven't clicked as an attacking force yet.
There is a significant rebuilding process that needs to occur, which wasn't necessary when Wenger took over.
And this being a WC year, there is even less time than usual to prepare for the new season. And we still have to buy and sell players, get a new coach in and get everything set up for the new season. It really makes sense to try and get the job of finding a new coach over and done with as quickly as possible or we risk entering the new season under a cloud again.