The idea of mating is silly and counter-intuitive

The idea of invalid moves of letting your king get captured in addition to the flurry of rules new players are thrown at such as complicated castling rules, en passant, pawn promotion and the way each piece moves is already overwhelming enough, which creates a barrier of entry to the game of Chess.

The additional rule that players cannot move their king into check and that their king cannot be captured but rather be "checkmated" is unnecessary and just increases the complexity of the game without increasing any of its depth. It is a counter-intuitive rule and the game with or without the checkmating rule is logically equivalent.

The only logical effect this has on the game is introduce the idea of stalemate, which is considered a draw, but as the general consensus already stands the drawing rate of this game is far too high which takes away from the sense of tension and excitement other sports have. 

Stalemate is also perhaps the most counter-intuitive form of drawing. You checkmate yourself on the wrong turn- which creates a draw? It makes much more logical sense for the side to get stalemated to be considered losing.

Anyway, the King should be captured instead of Checkmated is the idea I am trying to express here, as this is much more intuitive and logical for the game.

The only opposition I can see to this is that it undermines centures of tradition in chess, but is it really a big deal for a purely mathematical game? Chess had many revisions itself throughout history such as the introduction of the queen e.t.c. to improve the game, and just because it is the 21st century doesn't mean the game shouldn't be revised further for improvement.

You may find checkers a more agreeable alternative.