You’re ignoring the three other names I mentioned to just respond to the point on Fergie.
How did having a three year deal and the illusion of long-term-thinking prevent the players from downing tools under Ole, EtH, Mourinho and even Moyes (who had a six year deal!!)?
You’re also ignoring the fact that Carrick currently being on a six month deal hasn’t had the effect you’re predicting a one-year deal would have, even after coming in after a sacking of a manager that wasn’t sacked due to the players downing tools.
Giving Carrick a one year deal has many positive aspects for the club. It’s financially better in case they need to part ways. The players aren’t playing poorly because he’s only on a 6-month deal so the notion that a one year deal will suddenly make the players depressed is off the mark IMO. It gives the club the possibility to assess Carrick’s credentials under more realistic circumstances ie European football, full season, transfer window, squad management, and it gives the club another year to assess other candidates while not being as financially exposed by a long term deal.
If you think he’d agree to a one year payout on a three-year deal and that would signal more ”longevity” and not signal to the players that he might not be the long-term guy we might as well agree a 15 year contract with a one year payoff if he gets sacked. I don’t think he’d agree to that, because the entire point of the longer contract is financial protection for the manager.