Why are we not allowed to capture the King? Why do we have to corner the King in a checkmate? Why can't you kill him if your opponent did not notice that his king was in check? Because like in real life, killing the opposing King on a battlefield is not very profitable. It is much more useful to capture him alive and ask for a ransom, thus preventing a new King and getting a huge sum of money.
Also, in the era when chess was invented, playing a game where you won by killing a royal could have been seen as tantamount to a declaration of high treason.