I think there's some intrinsic value in having a manager who is in tune with their club's overall ethos, culture, and way of doing things - for that reason I think Solksjaer has an outsized value to Man United, all else being equal.
That said, I don't think he's doing enough right now. He's been fortunate to have a maverick in Bruno who can single-handedly run an attack (and did so at Sporting for years), which has papered over the cracks - the fact is that Ole still doesn't know what his best system is or how his players optimally fit into that. Just this year you've played 4-2-3-1, 3-5-2, 4-1-2-1-2, 4-3-1-2, 4-3-3, etc. It'd be one thing if Ole was freshly appointed and was getting to grips with the team, but at this point in his tenure it feels like he's just throwing ideas at the wall and hoping they stick.
I don't think you do enough off the ball - right now you don't have anything even remotely resembling a cohesive press unless you're well behind and throwing caution to the winds. For me there's a middle ground there, and there are numerous mid-table managers in the PL doing more with less for me.
Ultimately I think Solksjaer's strength is his ability to connect with players and to work within the hierarchy at Man United - tactically I think he's more or less a disaster and pretty comfortably the worst manager in the PL. The issue ultimately is whether his ability to motivate is sustainable and can overcome these issues - my suspicion is that the more and more Mourinho's toxicity fades from memory, the more ineffective Solksjaer will become.
If I were you I'd hire Allegri.