Most fatal errors just mean you lose an entire atomic update, and the type where you "successfully" write bad data imply the same sort of repairs as server-side maintenance would.
In practice, I think the biggest issue is that if you had to restore a backup, there'd be no way to restore only -your- tree, since the server doesn't know structure or ownership of the buckets. You'd have to roll back everyone in the bucket store.
I don't want to be too negative, because I think having something like this is a good idea. It's plain there are challenges to be solved here though.
Edit: though I do catch your point that N clients all maintaining the same index tree is potentially like having a non-redundant N-wide storage array--failure rate is cumulative. Think you could possibly mitigate this with a single-source-of-truth per table/index client-side design, but that's an obvious potential bottleneck.