I don't think i'm EtH in anymore and the obvious and truthful answer is not a damn thing, however...
I think the fear is that we slip back to being a low block/pragmatic team because I don't see what any top manager can do with the profile of this squad other than just be solid and grind out a top 4 battle, occasionally hitting the dizzying heights of a distant second or third place finish. Implementing real change is going to be painful. Each manager-Jose, Ole, EtH- has said and done the same thing, that he wanted to take the next step, be more proactive and it fails miserably.
Implementing real change doesn't have to be painful. Often times it isn't. The reason why those managers said so was to protect themselves. If you look at the best managers, they did not need pain. Sure, you won't get the best results, but it's important to remember that United fans are actually extremely lenient and only want to enjoy watching their football club again. Performances that get fans excited, then results can follow.
This very low standard has not been met by our former managers.
So what would anyone miss about EtH? Well, in theory, pressing high, committing many players forward, playing aggressively and with energy- which is what EtH is trying to get us to do- sounds quite entertaining but it's been undeniably crap so far. Could it work though with better players and a better structure? I'm very skeptical and i'm starting to think the answer is no. However, given some of the names i'm hearing linked with the job, I think i'd rather try another season of getting this right than some of the alternatives that have been put forward so far.
The reason why it's not worth it to persist with better players under his coaching set up is because there is no logic in his player selection, and what he values that would lead any fan to have trust in him to make things better. If growing pains should happen, fans can accept that if his player selection proves he believes in his setup will bring us long term results. For example, if pressing in his setup should be believed it's effective or at the very least valued by him, why select players like Rashford that hamper one of his system's advantages in the press? This suggests he's more pragmatic than he claims to be and one rightly questions if he truly believes his pressing instructions when followed bring the side rewards, or that it's tested enough in the league as being good enough for the future of his sides. Tested by having the proper player following instructions so that one can accurately gauge if it's effective or not in this league as he's new to this league.
Two, even if we forgive the above example and many other examples with his player selection contradicting his system, the fact that all the top sides, be it in all the variety of ways a top side that plays front foot/progressive football has played (A Klopp style to a more possession oriented Pep style), have valued compactness to defend transitions would lead any fan to question the legitimacy of his setup. This due to as I stated, referencing that all the top sides value compactness, or through the evidence of this season's awful defending performances.
There are 2 thresholds that he did not meet. Thresholds as in precedence from past sides, 1. in what they value and 2. in how long it took them to coach them to lend their sides' performances clear tangible advantages. Klopp's sides did not have results at the start. However, his coaching lent them clear advantages that were evidenced via statistics apart from the obvious observations any fan can see. At that point, it became easy to trust his coaching could bring better results if he was provided better talents.