Great analysis, but I think that the very fact that it is possible for people to move their BTC off exchanges (and indeed quite easy and is happening all the time) is a huge disincentive to institutions to engage in such manipulation.

The risks to them are so much higher because the percentage of BTC held on exchanges is actually very low - less than 11% of all BTC and many buyers (including big ones) are HODLers.

There is much greater transparency. It is not difficult to determine how much real BTC an exchange holds - its all on chain and traceable with the right tools.

Even a whiff of this sort of manipulation could cause a run of withdrawals and trying to shut down withdrawals would destroy the reputation of the exchange.