I disagree with the underlying premise. The chopping and changing of the squad is not inherent to changing the manager and did not have to happen, it is itself a result of bad management (not by Old of course). I mean, appointing Moyes after Ferguson, LvG after Moyes, and Mourinho after LvG - none of that makes sense in terms of continuity, and that's what caused the constant squad overhauls. (I'm not including the Mourinho-Ole transition here since that one did work out better. But since Ole wasn't initially hired as the permanent new manager, probably not much thinking went into continuity there either.)
Next, I also don't think Ole would have been instrumental in getting these players to join United. He is not an illustrious manager and has not achieved great things. He will have played a (large?) role in the player identification and hiring process, of course, but I would really doubt that big players would have joined United because of Ole in particular.
Also, you don't need these players specifically at United. It's a cool group to have in its current form, but another manager would also have been able to attract big names (probably some of the same), because United are a big club with big money, regardless of the manager. (And to some extent even regardless of performances, as some of the transfers during the worst periods of the past few years have shown.)
Finally, firing Ole wouldn't have to lead to another squad overhaul if United would do a good job with the selection process, and made sure to hire someone that can build on what Ole has been working towards, and agreed that the current squad is in good shape to continue that work. For example, hiring a manager focused on possession or pressing would make little sense. Of course though, as I said,.United had had an awful recent track record hiring coaches with an eye on continuity. So in that sense, if they would get that completely wrong once again, you're right that you'd be in for another squad overhaul that would set you back a few years again...