I wouldn't say no-one improves. Lindelof, McTominay and Rashford have improved over the last few years for example. Martial is a better overall player now than for Monaco (although his development hasn't been linear). Likewise I'd say James, AWB and McGuire have been integrated very well to the huge pressures of playing for United, which although isn't an "improvement" in the traditional sense, it's important.
Although when I said no one it was hyperbole, I don't think these examples are very good except Scott. In my view, both Martial and Rashford have stagnated, while Lindelof has only improved in comparison with his initial abysmal level. As for the new signings, it remains to be seen if they start to stagnate like the others.
In terms of whether he will press this has already been shown, as it was with Lukaku. Therefore Ole isn't going to waste his time trying to shoehorn him into being something he isn't. In terms of cutting out passing lanes he simply does not have the off the ball concentration, which again is proven.
If I remember correctly, the only manager he played under for us other than Ole was Jose, and Josse doesn't implement a high press. For Ole's initial winning run, I remember him pressing as well as anyone in the team. The problem was his recovery runs if the press was bypassed, he lacked that dynamism and thus Herrerra often covered for him. As for the bolded, I agree, and I think he should be working on that, as well as bypassing pressure with his 1st or 2nd touch, instead of trying to muscle through the midfield.
It's why in my view Pogba is such a square peg in the modern game. I see phenomenal teams and see how he could be phenomenal in them. However I see teams like Liverpool that are based solely on a system that requires every player to sacrifice themselves for the good of the team and just can't see where Pogba would fit in. I guarantee for example that Klopp would prefer Henderson to Pogba, despite the former being far less talented.
I can understand this view, although note that the Liverpool way isn't special. It's simply the least technical players on the team covering for the more technical players, that's all it is. For instance, in City's system, the fullbacks cover for their midfielders since KDB and David Silva are of that elite quality that requires that treatment. Just think how ridiculous it would be to play KDB and Silva as holding midfielders, so as to allow Zinchenko and Kyle Walker to fly forward.
Since we have Pogba and defensive fullbacks, we should be comparing our system with City's rather than Liverpool's.
And as for the bolded, make no mistake, every elite manager recognizes quality when he sees it, and the more astute ones are able to integrate that quality into the squad to the benefit of everyone. Gundogan, Sahin, Gotze, Kagawa, Coutinho, etc were key players under Klopp, so I highly doubt he'll turn his nose up at elite quality like Pogba.