The instance doing it is what makes this work at scale. If there are 10 big instances where most of the content is generated, the traffic between them scales linearly with the number of posts.

If your client is doing the indexing, not only is this a lot of computations for a phone that runs on a battery, but the amount of traffic for each server scales with the global number of users, which is untenable for most servers.

If you really want to be immune to defederation (not quite literally, but in the ways that matter to you), your solution is to deploy your own home instance and federate with communities you browse. This is the client that will be doing the indexing. Of course you can get individually defederated but if you're not a nuisance I can't see why.