Chess has been extensively play tested and the balance is peak.

Technically, chess ends one turn before the king is taken. "Checkmate" basically means, "I can capture your king next turn of I want to and there's no way you can avoid it."

You're not allowed to put your own king in check because, if this were allowed, stalemate wouldn't be possible; the game would always end with the loser moving their king into check and the winner taking it. The rule allows the player of a losing game to still play for a draw, as opposed to simply resigning.

Had the game not announced this, I wouldn't have known.

Sounds like maybe you need to practice more.

Why, besides supporting your inability to properly apply the rules of chess?

You and your friends can set any rules for any games you play, as long as you agree to the rules together. Sometimes it's fun to try and change the rules.