Yes I'd agree that it is impossible to prove something to someone you don't share common ground with.
I'll never be able to prove ghosts don't exist to someone who believes they do.
I might however be able to prove the absence of any evidence for the existence of ghosts, provided that the person I'm speaking to has the same perception of what constitutes evidence.
I think it’s extremely easy to prove that a covid infection is more harmful than the vaccine in aggregate in every demagogic.
Honestly that is probably the case even if you are only counting post-covid symptoms [1].
1: https://www.cambridge.org/core/journals/antimicrobial-stewar...