But isn't that exactly how staking works all over the place? You have to lock the coins for X amount of time, send them to an exchange, and you can't get them back until your staking period expires. The safety of the keys has nothing to do with it.
I've only staked a worthless altcoin, where staking worked straight from the Bitcoin Core clone, without exchange. I assume the same would work on ethereum, but the minimum is about half a Lambo worth of that coin. So staking leads to further centralization, who would have thought.