We also don't do this. In a near future implementation you can just synchronize the end-to-end encrypted search index.

This step is what I was expecting you to talk about, and it has some tricky subtleties to get right, which is why I looked for it in the whitepaper.

A trivial problem with a naive implementation is being able to perform presence proofs using side channel information: send someone mail containing a terms you want to verify, and watch for the associated high level costs affecting operations that are likely to be incremental index change uploads.

You mean you currently do this but plan not to in the future