Using gpg via webmail while you can use any gpg enabled mail client is just wrong (imo). Mailpile can be (and should be) installed on your own machine to provide best security. We have not yet look into mailpile in detail (though it does support autocrypt which is awesome) as we always thought of it to be a mailclient (although built on web technologies) to be rather installed locally then as a webmail of a provider.
As we are considering switching webmail (or providing two) mailpile is definatelly something to look into.
Rainloop provides gpg support too, although not as good as mailpile i suppose. I'm guessing mailpile does not wipe your gpg keys when you logout. It's all a matter of how you look at things. Our current standpoint is that webmail is rather on the go solution, when you dont have access to your device on which you are running your mail client (evolution, thunderbird, k9 or mailpile). In this cases you do hope that your key you used (eg. form your usb stick) is not going to stay forever on someone else computer. This is the reason we have picked Rainloop.