I support this idea, but I wouldn't touch something like Tutanota or ProtonMail that doesn't support an open standard like IMAP (or doesn't provide it for the free tier or has "bridge" applications to install) for saving and archiving mails offline on a computer. Tutanota and ProtonMail are both walled gardens of their own making. I can't easily migrate out of Tutanota (or ProtonMail if I'm a free tier user) and take my emails elsewhere. I appreciate that they provide (or claim to provide) better encryption, but I like to have control over my data and where I have copies of in an easily accessible manner.

I'd suggest instead, for much cheaper, Posteo.de, Runbox.com, Mailbox.org, Mailfence.com or Migadu.