As always, there's a relevant XKCD https://xkcd.com/538/
If Person B published a message under Person A's name, that is, to the non-crypto world, a faked post. They're not going to be impressed by your argument that actually it isn't faked, it's real, Person B just had access to Person A's computer.
Happy new year.
I'm not making a comment out of pedantry, I'm telling you how I expect this is going to be seen by regular users. People on the whole are not interested in whether or not some particular security system is theoretically perfect, they're interested in whether or not it actually provides the security that they interpret it to promise. And they will interpret your claims as meaning that messages cannot come from anyone other than the signed user, which is going to be a problem the first time that assumption fails. And it will fail, because people aren't good at keeping secrets secret.