Both models can work, but I feel like Man Utd's recent approach is similar to Chelsea's. Managers get given the chance, but if it isn't showing enough promise or direct results they get fired. Ole started as the latter and then showed signs of the former, but now both seem to not cut it and a firing seems close.
For a long term coach it's important to have someone who can build something up, while starting out with a strong base, but while also showing the capacity to reinvent themselves and alter their team's approach. A people's manager tends to work for a while, but not forever (i.e. Ancelotti can be great, but usually loses the spark after 2-4 seasons), a coach with a defined style seems to work for a single season or perhaps two MAX, especially in the past decade this seems to be the case to me. Mourinho or even someone like Bosz seem to be outdated if you're looking for a longterm manager, though they usually show great signs that make you think their best seasons are still in them. Wouldn't be surprised if both are out of Roma and Lyonnais sometime between the end of this season or halfway in the next.
What seems to work in an almost timeless manner is the adaptable but adamant coach. I think Ferguson was one of these, though he also had a good team around him. But even though United had a certain identity, SAF wasn't too afraid or narcissitic to tweak things when necessary, depending on the team's quality, balance, opposition and simply the nature of the current game. Nowadays there are a few as well. Klopp, Guardiola, Simeone and Ten Hag have clear views on football, but they're not as stuck to a very specific approach as people like Bosz, Koeman or De Boer (I'm Dutch so those examples get blasted in my face much more than other nation's coaches) are. Klopp has his fast-forward approach, but the way it's implemented exactly changes around every 2 seasons or so. Guardiola is more about possession and quick combinations, but during certain momentums it's a more classical 4-3-3 and other times players like Messi and Foden are strikers and Bernardo's are close to defensive midfielders. Ten Hag is somewhere in between them, and generally favors a 4-3-3 that can morph into a 4-4-2/4-2-4, but now figured an anchor man works better if you have shorter (though very talented and technical) center backs. Simeone says he bases it on the club's identity, and I've only followed him at Atleti, so I'll take that as his own identity for this discussion: he focuses on hard work and counter football with a solid defensive base, preferably in a 4-4-2 formation. However, he buys more offensively capable players every year since the Raul Garcia's and Saúls don't cut it as your offensive midfielders if you want to not just shake up the top, but become on if its members. Since last season he even implemented a much more possession based tactics (he argues to bring out the best of Suarez) and the 3-4-3s and 3-5-2s and even occasional 4-3-3s are something you couldn't imagine of him two years ago. Furthermore having players like Lemar as CM, Koke and Rodrigo de Paul as the defensive midfielders is something I didn't see coming, but it shows Simeone is willing to think about and try out alterations to his team.
All of these coaches' teams have had drops in quality for a season or so, but there were clear signs they were working on something, regardless of which players were bought or not. Last year Klopp's Lpool was rusty, but this season they're back. The season before that City was vulnerable and now they have two very solid seasons in a row. 17-18 Ten Hag was shaky, 18-19 was amazing, 19-21 seasons were a bit inconsistent and this season they seem even stronger than their 18-19 shake-up. I think I've talked too much about Simeone in the previous paragraph, but same story there (although they have lost their unsurpassable wall in defense, which I hope they can implement into this offensively very sound squad).
Ole seems to be the people manager type, especially the way he talks about his 'leaders' and the yadayada. I had faith in him, especially with the team he has behind him, but it's almost like he has a few tricks up his sleeve, but when the opponent isn't shaken, he's got nothing. You can't rely on a few tricks if you're here for the long haul, no matter how good those tricks are. You can't just keep your group of players happy and a team and then if the players are good enough that'll get you titles. Maybe that worked before, but it doesn't now. I know Ole means well, but I don't think he is a long term manager like that.
And when coaches start talking about necessary transfers instead of working with what they have... then what exactly do they add as the coach?
To be honest, I don't know which category Zidane belongs to. He did have his CL titles during his first spell and I think one LL title in the second? He did show differing tactics all the time, but general approach wise I'm still uncertain about his long term validity. Even with those titles, a lot of those seasons Madrid were pretty shaky. I don't think Rodgers is strong enough for a club as big as Utd, but he has shown more of the consistency, adaptabilty and flexibility that I think are necessary if you're thinking about long term managers. It's just that his Liverpool spell showed that he might miss the final touch that'll get you silverware instead of the silver medal peak.
So options wise I think Zidane would be a gamble, probably a better people manager than Ole, but still a risk in the position that Utd find themselves in. Ten Hag if he's a real option would be good I think, although so far his biggest club has been Ajax (if you don't count his stint at Bayern's second team, of course). But does he want to? Does he want to for a long time? Klopp, Pep and Simeone are probably not coming at all. So out of managers linked right now, I think only Ten Hag shows the promise of adapting the team and improving the players past the quality they already had when bought.