user17817: The objective of chess is to put the opponent's king in a position where it cannot evade capture. Why not go all the way?
Short of tremendous blunders of moving into check, chess would be completely the same, except with one more move at the end, and the rules would be simpler and easier to explain.

user16771: Of course the goal of chess is to capture the opponent king. However, I see no point in your suggestion for the game. If one player’s king  is in check they are forced to move a piece so your king does not remain so. If you are checkmated, by definition, your king cannot move and so you cannot escape the check. Because no move you could possibly make would avoid that, there is no legal move for you and so it is game over.
So all in all, you cannot simply move any piece so you get checkmated in the next move because a check forces you to escape the threat of check.

user12629: 
Short of tremendous blunders of moving into check, chess would be completely the same

But it wouldn't be the same. There is one case where moving a king into check would not be a blunder. That case is what we currently call stalemate. If it was legal to move a king into check, then almost all cases of what is currently stalemate would instead be a win for one side.
This would have a huge impact on the endgame. Many endgames which are currently draws would turn into wins for the side with more material (KP vs K would win regardless of opposition, for example, and many other endgames can be simplified to that) and many theoretically won but difficult endgames would be much easier to win (since KNN vs K would now win, KNN vs KP could be won by just taking the pawn.)
And this effect on the endgame would in turn have a large effect on the earlier stages of the game. It's harder to sacrifice a pawn if you know you don't have drawing chances in the event that you end up a pawn down in the endgame.
You could, of course, hack a stalemate exception into the new rules, but that would probably be even more confusing.

17817: <p>The objective of chess is to put the opponent's king in a position where it cannot evade capture. Why not go all the way?</p>

<p>Short of tremendous blunders of moving into check, chess would be completely the same, except with one more move at the end, and the rules would be simpler and easier to explain.</p>
 16771: <p>Of course the goal of chess is to capture the opponent king. However, I see no point in your suggestion for the game. If one player’s king  is in check they are forced to move a piece so your king does not remain so. If you are checkmated, by definition, your king cannot move and so you cannot escape the check. Because no move you could possibly make would avoid that, there is no legal move for you and so it is game over.</p>

<p>So all in all, you cannot simply move any piece so you get checkmated in the next move because a check forces you to escape the threat of check.</p>
 12629: <blockquote>
  <p>Short of tremendous blunders of moving into check, chess would be completely the same</p>
</blockquote>

<p>But it wouldn't be the same. There is one case where moving a king into check would not be a blunder. That case is what we currently call stalemate. If it was legal to move a king into check, then almost all cases of what is currently stalemate would instead be a win for one side.</p>

<p>This would have a huge impact on the endgame. Many endgames which are currently draws would turn into wins for the side with more material (KP vs K would win regardless of opposition, for example, and many other endgames can be simplified to that) and many theoretically won but difficult endgames would be much easier to win (since KNN vs K would now win, KNN vs KP could be won by just taking the pawn.)</p>

<p>And this effect on the endgame would in turn have a large effect on the earlier stages of the game. It's harder to sacrifice a pawn if you know you don't have drawing chances in the event that you end up a pawn down in the endgame.</p>

<p>You could, of course, hack a stalemate exception into the new rules, but that would probably be even more confusing.</p>
