Is there a reason you are putting limits on defining facts like this? Most games I play have flexible GMs, and I define facts (both beneficial and detrimental) on the fly for my characters. Of course, making sure things aren't broken/stupid are up to you as the GM - ie: a player couldn't declare themselves as a king (depending on setting/tone), for example, but a prince or exiled royalty would be more likely.
If you do want to use points and/or want to maintain a balance, I would recommend the story point system in SWFFG - where a player can spend a lightside point to define a beneficial fact, which turns into a darkside point the GM can use to define a detremental fact later. That way, players get their points back, and the story gets more interesting overall.
Mask of the Rose Has Just Launched (www.failbettergames.com)
me_irl (lemmy.ml)
Help me save a darling system
Story Points...