Let’s look at the stat you brought up: since Carrick’s arrival, Arsenal, Chelsea, Liverpool, and Forest have won 4 games by more than one goal. United is tied with City and Brighton at 3. I would say this is not as bad as you implied? Meanwhile, Iraola—the supposed master of progressive football—has only won one game by more than a single goal. Now, you could say that Bournemouth doesn't have the same quality of players as United, which is fair. But if "doing more with less" is the standard, why aren't we calling for Hürzeler instead? He also has a "lower-profile" squad at Brighton, yet he has a better league position and more multi-goal wins than Iraola.
Ultimately, the data tells us one of two things: either the entire league is so bad, or the league is so competitive right now that nobody is beating anyone easily.
Let's look at other stats. Since Carrick took over, United has earned the most points (potentially second if City win their game in hand) and scored 24 goals—tied with Arsenal at the 2nd place and only Liverpool has more with 25. I don’t understand the constant complaints. Do people sincerely believe we have a top-three squad? Before this run, nobody imagined we’d even be fighting for Champions League. If Iraola is working miracles, then so is Carrick.
You mentioned Carrick is "running above expectation and it could quickly fall back." Of course, these results feel unsustainable — but that’s not because of the coaching — it’s because we are, at best, a top-six squad currently playing at a top-two level. If we are “only” fighting for top 4 next season, would anyone say it’s a failure? The double standard here is also particularly strange: if Carrick is overachieving and bound to fall back, why is the same not said for Iraola? Why are people so certain Iraola can sustain his level at a bigger club? For the past few years, the narrative was that United was "too big" for managers like Ten Hag or Amorim. How can anyone be certain that Iraola is a "sure upgrade" when he has zero experience at this level of pressure?
We need to set a baseline: unless there is a miraculous summer window, the proper expectation for next season is to fight for a Champions League spot. If the head coach hits that target, they've done their job; if not, they move on. While that feels like a "downtrend" compared to our current results, we should agree that it's a realistic expectation for Carrick, or anyone else.
If we somehow land Enrique, I’m all for it. But I don't see a logical reason to favor Iraola over Carrick that much right now.