To the best of my knowledge there's not even any known mathematical theorem that would prevent such algorithms on regular computers. I don't see how this would be any different for quantum computers.

That is correct. Any proof that digital signatures are secure on classical computers would imply P != NP.

Further, it is known that BQP (bounded error quantum polynomial time. The quantum computer equivalent of P) is contained in PSPACE. However P=PSPACE is still an open question. This means that we still do not have any theoretical proof that quantum computers are more powerful that classical computers.