I'm not talking about the technical rules of legal moves when your king is checked. I'm talking about when there's checkmate and the victor and the loser are set in stone. Why can't I capture the king at that point? I can understand why you can't do so with a resignation because your pieces likely aren't near the king.
You can, you're just being socially pressured not to.
If you have the guts, you absolutely can just take the king. What are they gonna do? You have the king.