Family Bulletin Board is broken. Can't clear it. No Mods Installed.

Yes it has been broken since one of the latest patches. There is a mod to fix it, but it seems like you don’t use mods. Hopefully it gets a fix soon.

You can click “me too” on this report of it.
https://answers.ea.com/t5/Bug-Reports/OPEN-PH-clear-bulletin-board-doesn-t-work/m-p/6882955#M64509