You can totally search email contents with ProtonMail -- it just does it clientside. I just tested with my 125MB of emails and it was fast (under 1s) but maybe if you have more emails it could be slower.
That is what I'd expect, since obviously they cannot build a search index over text they cannot read. Transferring the entire contents of your emails to your web browser to search locally would be slow and impractical on anything but a very fast connection.