Once you have to index or parse the email for search, it can no longer be stored as ciphertext, that is, end to end encryption interferes with search.

At best, you could search headers if they aren't encrypted.

Until a viable ciphertext search scheme arrives. (there are some, but everyone I've seen has some caveat or hole)

You could do everything client side as well and just store encrypted indices on the server. Probably not a good idea, but not the end of the world.

I don't think users actually care though. Google's attempt to redefine "end-to-end encryption" to include decrypting something mid route bothered me. This... meh.