Does this Time Format exist in chess? If no, then why?

A chess time format where each player is given a fixed number of seconds to make each move. The timer resets after every move. If a player fails to move within that time, their turn is forfeited, and the opponent immediately gets to move again. This introduces a new strategic element — the option to not move in certain positions, turning inaction into a tactical decision.

Hmm. I have never heard about it except in a short story.

Which short story? Also, do you think it will be a good idea to implement?

"All the King's Horses" by Kurt Vonnegut.

It's not quite your arrangement but it offered an interesting game.

I just read the plot, it is a fine story and can make a great short film. However I could not see its connection with the time format I am suggesting.

This certainly

This certainly would make up for a good time setup for chess, I'd suggest you to go to the chess

go to the chess.com discord server and post it as a suggestion

The time limit was ten minutes per move and the 16 Americans were human Chess pieces.

The penalty for overstepping the time limit wasn't stated but I assumed it would have been game over or at least the execution of one of the players.

More than a time control this sounds more like a variant, some sort of chess with move skipping.

Really?

This runs into a small problem if you end up in a mutual Zugzwang position.

For example:

In this position, the winner is the player whose turn it isn't. But since both players will likely realize that and continually forfeit their turns indefinitely, it turns this won endgame into a draw. However, this could most likely be fixed by forcing a player to move after they forfeit a certain number of moves in a row; if they run out of time after that, they lose on time.

I know this position. White wins if it's black's turn to move and black wins if it's white's turn to move

Great observation.