Protonmail seems to pull it off. Though at the moment encryption only works inside their system. They are actively working to implement the ability to send secure messages to people outside their service with GPG, though. I believe the CEO said it’d be ready by early 2018.
Please correct me if I'm wrong, but they don't let you search in a protected manner.
They enable searching of data they keep unprotected (the metadata so to speak)
And proton mail bridge seems to be an "offline" (i.e. offline to them) email search engine that you run yourself, so it downloads your emails, and makes them fully searchable, but to do that, is also keeping them in an insecure state.
The local stuff isn’t necessarily insecure (depending on your paranoia level). The security of your computer system is totally unrelated to the encryption of your mail - even with GPG most people are keeping their private key on the same system they use to read their mail. Full disk encryption with something like Veracrypt or bitlocker or file vault or LUKS should be more than enough to keep your decrypted emails safe when you are not using your computer.
My guess is that bridge is run as a service. i.e. you make reuests via web site which are encrypted with local javascript (so that proton mail can't interpose), protonmail forwards to the service user runs which provides an encrypted response which local javascript then decrypts and displays.
In that case, you have to run a service that is always running that is effectively keeping the e-mails available in the clear. Is it better security than keeping them in the clear on a central server? sure. But is it really any different than running my own smtp/imap/webmail server on aws without encrypting any emails which I access? In practice it would seem to be a similar threat model and I'm not convinced many would view that to be particularly secure, just a tad more private.
