Yes it could work. But the Steem protocol would need to be changed to create such a system.
Everything is currently public and stored in plain text. (Except the passwords of course).
Your entire history of comments, posts, new followers, upvotes, resteems and powerdowns, are available for everyone.
So implementing a 'pm' system would be tricky. Because it's impossible to 'hide' data in the current system.
for example
Someone could create an #SMT (Smart Media Token), with a closed ledger. Were you can store messages in a way they aren't visible for everyone.
I see what you mean but this makes it more private.. I could just be a simply cryptographic message that every steemit user has the key to decrypt or an only steemit users kind of tag that prevents steemit.com to publish the content to non users.. (like nsfw for example)