Doesn't Google Voice solve this problem? Or perhaps there are restrictions I don't know about. Of course, you still have to remember to create a burner phone number before giving out your contact info...
Only sort of. I wouldn't be surprised if Facebook rejects Google Voices numbers and will only accept a real-live carrier numbers. It seems pretty easy to do, given how often my GV is rejected by sleezy services I'd like to give a throwaway (e.g. peoplesearch opt-outs).
However, I'm not going to personally test this theory by attempting to give a panopticon like Facebook even my semi-throwaway GV number.
That would solve the issue voiced by OP
If it never occurred to you that this could happen, you would not take steps to prevent it.