There are 3 wealthier clubs in the league compared to us (two of them considerably so) and Liverpool/Spurs are not far behind especially with their increased stadium capacities to come plus CL football.
So we are not exactly in a position in which our wealth by itself counts for much more then being able to remain competitive in the top4 race.
We also have a pretty average squad which is not underachieving for the most part. The team we played yesterday for example is just really really bad.
Top 4 would be the expectation of a new manager but he'd have to come in and hit the ground running. If it's someone which is big on tactical training for most of these players it would be a huge huge change in how we operate.
A bad season in which we finish 6th or lower is not out the question Liverpool, Chelsea and United have all had these seasons.
Even if we hire a top manager that alone isn't enough to guarantee top 4 or a championship. Let's say we sign Allegri he's still going up against Conte, Guardiola, Mourinho, Klopp and Pochetino all of them outstanding managers in their own right all of them will have budget which are in the same bracket as us or higher and all with squads which are comparable or better.
For a new manager to come in and be successful we need his tactical ideas to succeed in a league he most likely has never played in, we need to successfully improve on our current squad in the transfer market which even with the best intentions is not always possible and we also need some of the teams around us to hopefully underperform.
I know it's easy to say Wenger has done so much wrong and we are 4th therefore things should be better with a better manager (on paper) but I think the reality is even with Allegri, next season would be walking a tightrope it could easily go horribly wrong.
I'm more than willing to take that risk because I'm fed up, I don't like watching us (honestly only watched a handful of full 90min games this year because it feels like it's irrelevant anyway) but I really think there's no reason we are more special than Liverpool or city or Chelsea or united and with a new manager and how competitive the league is I think there's a pretty big chance we have a poor league finish, in which case fans expectations will align and we spend more time looking for tactical improvements which would serve us well for the long run in the same way Liverpool and Spurs fans got excited seeing Klopp and Pochetinos changes to the side despite being in a poor league position.