> I think a full index of the contents of hundreds or thousands of emails and their attachments is soon going to take a lot of space and be slow on a mobile device.

I initially read “hundreds of thousands” and would have agreed that it might be a problem for those rare users (not even sure about that), but no, “hundreds or thousands” is a trivial amount of data. Normal mailbox operations already need to synchronize state; you just apply index operations along with this. (As for indexing PDFs and images, I don’t expect that in a basic implementation, or maybe ever. Doesn’t mean the entire feature should be missing.)

Which is why other services (e.g. Tutanota) have already implemented it, and also manage encrypt things like subject lines, which Protonmail doesn’t (!).