What does encrypted mean ?
I've mainly seen Flarum used as a public discussion platform. I don't think it would make any sense to encrypt data (on the server) that's already displayed publicly for everybody ?
I suppose this comes into play in private messages or group discussions ? I suppose that's something you could implement in Byobu, where each client encrypts the messages so only the other recipients can decrypt it.
We've already discussed the fact of hiding Byobu discussions from admins earlier (must be in the extension discussion) and it seemed that it's usually something not wanted at all. Often admins or mods want to be able to access that content to do their job. So adding another layer of difficulty for mods to read private message will probably be a feature most forums don't want.
Quickly reading the link you posted I don't understand how those password-protected topics work. Are you expected to share a password with everybody who wants to read your topic ? That sounds very annoying.
While we talk of encryption something I would find cool would be to have all messages signed. Create a private key for each user that is decrypted client-side with their password and sign all posts. Though not sure if that would be useful at all. Just cool ?
Whatever you do with encryption you must trust the medium. You can't trust a website to do exactly what it days it does or to be the same when it says it didn't change. What I want to say is that if you want to use an encrypted forum, you will likely need a client application whose code you can clearly review and whose updates you can control. In particular if the goal is to prevent the owner of the website to read the messages, this means you can't trust it to serve you a front-end that actually encrypts everything.
Flarum isn't any of that at the moment, though it's so extensible it would be a great base on which to build a fully encrypted ecosystem.