depends on the type of institution but I think there is a lot of cope and hopium around this. wherever there is fiduciary responsibility, there is dramatic risk aversion. and it's not like that's a fiat invention, it exists for a good reason if you want to have any principal/agent risk in a complex financial system. what I do think is exciting, however, is multi-institutional multi-sig, which has no analogue in fiat and potentially gives those in that position the best of both worlds (or decent of both).

the more bullish answer is that wherever you don't have that risk to address, people will probably learn the hard way that they should indeed hold their own coins.