Be careful what you wish for
We had a manager that got us in champions league regularly.(Rafa)
The first time he didn't he got sacked and we have only managed to do it twice in 7 years since.
Look at United after their long term manager resigned.
Utter chaos, awful style of play spent half a billion pounds on average players.
Err and only won 3 trophies this season
When Rafa was your manager (2004-2010) there was only 4 teams that regularly finished top 4 - Arsenal, Chelsea, Liverpool & Man Utd who had the experience and mentality (won one or more League cup, FA cup or League title in those 6 years). Since Rafa was "sacked" Man City & Tottenham have regularly taken that top 4 slot because football has moved on with either younger managers with new ideas, better players, tactics and last but not least money.
Every manager will leave a club either due to their decision or not (moves on, retire, sacked or pass away), for the last 10 years Arsenal under Wenger has not really improved just been consistent, our average league points for the last 10 years is 74 points, our highest was 83 (finished 3rd) and lowest 68 (finished 4th) in those years. BTW we finished 2nd last year with 71 points which shows you how poor most of the top 4 teams were - Leicester won it with 81 points.
Although Wenger did not always have the money to spend like the other top 4 clubs (due to the stadium debt), when he had the money he did not spend it or did not spend it wisely which all managers make that same mistake but he did not address those mistakes until it was too late. 3 FA Cups in 10 years is good for some clubs (you only have to win 7 games to win a cup against part timers or a rival Premiership team) but just winning a domestic cup is not good enough for any top European club which we are suppose to be.
No doubt both Manchester clubs will spend big and improve next season as they will get the players they need to win the Premiership or go further in the Champions League, if we get a new manager I don't expect him to win us the Premiership or Champions League during his time here but to improve us defensively and offensively every season which hopefully moves us up the league table year after year and/or get us further than the last 16 in the Champions league.