I banged my head about this 10+ years ago. In theory it is possible to to E2EE webmail, the trick is creating and encrypting/decrypting the mail private keys in javascript on the client side. It actually shouldn't be that hard to verify once, but the problem is that you really have to verify the code every single time it gets served to the end user, which is just about impossible.
That said, I use proton mail with their bridge https://protonmail.com/blog/bridge-security-model/ which in theory is a lot easier to audit, and the end user is in charge of when it gets upgraded, so a warrant in theory doesn't just allow them to flip a flag somewhere and have the client forward the encryption keys. Whether or not that functionality is buried in the bridge is something that could be audited, although i've not done it and frankly probably no one else really serious has done it either since the effort to audit it is more than just setting up a custom GPG configuration.
Edit: And just as a note, frankly it hard to justify not having an encrypted email/dropbox/whatever these days. I use it fairly regularly to communicate with my bank/attorney/etc. Its easy for them to use, and throws up another barrier to the bad guys on the internet that don't need to know my social security number/bank account numbers/etc.