I feel

unless the exchange puts it into a savings account, of course, but in that case it seems likely that they would have to offer some staking reward as part of such a change in order to avoid looking bad in the eyes of their customers

is a big assumption. Especially when we use it as a tool to control the HBD peg. It might fluctuate widely. Do you think exchanges even want to try to explain this added complexity to their users? Do these users care?