Isn't a lot of that just the suckiness of the IMAP protocol? Mozilla is pushing to add JMAP support to Thunderbird, and they're planning on using it in their upcoming Thundermail hosted email service.
Having to retype the search phrase is just a plain old ux bug
I get this, but most email is through Google and Microsoft in NA, at least, neither of which seem to care to support JMAP at all, on fact they are getting locked down more and more.