Why not allow King capture?


Hello Sarah,
What I mean is that player A should be able to win the game by capturing player B's king if either:-
1. Player B does not notice that they have been put in check (this would require that having to say 'check' be removed from the rules for OTB games)
2. Player B accidentally blunders and puts there own king in check (currently if this happens it is illegal and the move must be retaken).
In each case player B has blundered but gets away with it by being forced to retake the move. I don't think player B should get away with it. I think player A should be able to capitalise and win the game.
What do you think?

Requiring a player to win by checkmate, rather than by simply capturing an exposed King, means winning requires more skill and effort than otherwise. I rather like that the winning bar is set a little bit higher.
(That said, in some OTB blitz rules it is legal to capture a King that is in check.)

Thank you for your support Sarah.
I guess Landloch has a good point too. It can give someone an easy win if they can capture a king accidentally left in the open or unguarded.
I would maybe suggest to chess.com that the Blitz rule of being allowed to capture the king be applied to rated Puzzles (formerly tactics).
I sometimes blunder badly in rated puzzles by forgetting or not realising that I have been put in check. It feels like I am being let off too easily when I get another chance because the computer won't allow me to overlook the check.
I think king capture is allowed in the high speed variations, so you lose the game if
1. You don't notice that you have been put in check
2. You accidentally put yourself in check (is that possible?)
and your opponent capitalises on the error.
It seems like it would make the regular game more simple and elegant of these 2 situations were also allowed there.
Surely there are frequent situations where players end up doing either 1 or 2 in regular non-speed chess by simple blundering. But they are given an unnecessary lifeline by being allowed to take the move again.
Why should they not be put to the sword for such a blunder by allowing the opponent to capture the exposed king?