HIVE savings wallet earning a portion of inflationary staking rewards seems plausible to me. It would have to be a lot less given that it is staking for only 3 days vs 13 weeks (or 7 if you average), but some reward makes sense.
Implementation could be somewhat challenging.
Even at a lot less, it would be interesting to have it sit their earning something, rather than on exchange. since staked, it owuld be able to get something like 15-20% a year through voting, I think that without governance power and still leaving the reward half of the activity in the reward pool, it could still return a decent percentage. Paying out in liquid HBD daily would also be attractive for many people.