If twitter created some arbitrary rule like "We're going to fact-check all state/government personnel.", then the state/government personnel would just change platforms.
it's a real issue -- it's potentially more dangerous to push politicians to lie on platforms that fact-checkers can't respond and provide feedback towards, and if twitter starts playing hardball against politicians that's exactly what will happen.
A ton of small echo-chamber communities that splinter off as a result of perceived hostility or discrimination from twitter (but really any social media group) and the general public may be more hostile/dangerous than having these groups of people being vetted by the public at large constantly on twitter or other popular platforms.