In general the crux of most teams is the central midfield pairing. If you know you're leaving I think it's absolutely fair to hold off a couple years and leave the cash/decision up to the new manager. If you buy a central midfield pair one year then leave, a new manager in most situations will be stuck with that central midfield pair for the next 4 years.
The problem was Moyes tried to get a completely unavailable target as his main guy, and a completely unqualified not good enough midfielder to partner him with.
Fabregas/Fellaini would have been 50% of a good partnership but he wasn't available.
If Utd had bought in summer a top notch creative central midfielder, one who can play midfield, who can defend, tackle and has some strength, and a proper defensive midfielder, Utd wouldn't be in the position they are in right now.
Carrick for 5+ years hasn't been good enough. Many pundits highlighted how little Carrick did defensively, players can jog, hell WALK past Carrick with nothing. He has no strength, awful positioning, poor tackling, no pace at all. He just kind of stands around watching play happen, he is truly awful and no idea why anyone remotely thinks he's capable.
That wouldn't fix Utd's problems all told, longer term replacements. But the club has required a new central midfield pair for 3-4 years, the money was in the bank waiting to be spent, a manager was appointed and frankly the most important job he had to do, the thing that would make or break his time at Utd was to establish a new central midfield partnership to take Utd on for the next 5-10 years. He failed miserably, I think he/others have made the excuse that he expected to spend 6-12 months with the team to establish where the problems were.
If you need 6 months to realise Carrick/Cleverley weren't the answer you shouldn't be in football. All the more embarrassing was that Moyes tried to buy Fabregas/Fellaini throughout the summer... so the excuse he needed time doesn't hold, he tried to do his main job straight away.
However I pointed out at the time, Moyes was making quotes(paraphrased but VERY close) along the lines of "it's utd, there is no budget, and everyone wants to sign for us, you just pick and choose here". He had this seeming idea that Utd was easy street and he'd done a harder job where no one wanted to join everton but tell Fabregas he's wanted and he'd come a running.
He over estimates how good Fellaini is, (without descending into it again please people) Fellaini should have conceded a penalty in the opening minutes against Liverpool. He is always chasing the game, rarely ahead of it, he's a huge clumsy oaf and no where near good enough to be a DM at a top half of the table club let alone top 6. He looked at his best(which wasn't brilliant) as a lone striker in the early months of last season and looked worse as he was played deeper throughout the year.
Ultimately that he went for the completely 100% unavailable Fabregas, and did buy the absolutely 100% not good enough Fellaini suggests he isn't the right man for the job, amongst his many many other failings those two things stick out.