Saying "my character thinks xxx about yyy" is removing something from the game that should remain in the game. People don't bother to roleplay their character as a schemer; they just come on the forums and say "my character is scheming, ha ha ha". It's a shortcut and cuts out the players they are playing with, in the game.
I don't see this.
First of all, it seems to me that it doesn't "cut out the players...in the game", it cuts out the would-be schemer
from the players in the game. Because if the whole point is to take a shortcut to give characterization to their character, and the only people who will be seeing that are the ones on the forum...then most people won't know about this supposed character trait, and it won't matter.
Second of all, I have never seen anyone do this. To the best of my memory, I have only ever seen people explain their character's thoughts when people have posted explicitly stating that they are either confused about what the character thinks, or that they think the character thinks something else. (Or when there's a thread that's just generally people giving their character's opinions about something...which, again, seems pretty darn harmless.)
To me, this seems to be one more instance of trying to prevent behaviour that
has never actually been a problem.