Not sure about Posteo but at least Mailbox.org allows you provide public key and all the email coming in will be encrypted with your public GPG/PGP key. So you

Not sure about Posteo but at least Mailbox.org allows you provide public key and all the email coming in will be encrypted with your public GPG/PGP key. So you can only read them in your mail client with GPG support. Yes, mailbox could create copy of your email before encryption. But assuming that they don't/didn't so far, in case they change their mind the historical emails will not be accessible. The other solution where they keep private key (pass protected), well sure, that pretty much open for abuse but at some level you have to start trusting the law, otherwise everything false apart.