Edit: obligatory explanation (thanks mods for squaring me away)...
What you see via the UI isn't "all that exists". Unlike Reddit, where everything is a black box, there are a lot more eyeballs who can see "under the hood". Any instance admin, proper or rogue, gets a ton of information that users won't normally see. The attached example demonstrates that while users will only see upvote/downvote tallies, admins can see who actually performed those actions.
Edit: To clarify, not just YOUR instance admin gets this info. This is ANY instance admin across the Fediverse.
Wouldn't it be pretty simple to just encrypt them with the user's password? Or rather, create a key that's generated from the password, so you don't have to store the actual password in cookies, and then just decrypt it on the client side?
There will probably be issues with handling password resets, but other than that it doesn't sound too hard to implement it, unless I'm missing something, since my knowledge of crypto isn't anywhere near good. Should be one AES call, the way I see it.
EDIT: Oh, I've forgotten that you also have to somehow encrypt the messages that you send to someone, so a asymmetrical encryption is required, and that would be way harder. Or, maybe just store a public key, and encrypt the private key with your password, which is loaded into local storage and decrypted with your password once you log in? Still, that's not as easy as I thought.