Can there be a variant where there is a move clock rather than game clock?

I would love an additional variant where you don't have a game clock, you just have a move clock (like NBA shot clock.

You have to make each move within that alloted time or you flag. The time doesn't roll over. I think this would be a fun option

This has been discussed multiple times. It could be simulated with 0+X time control under "Bronstein delay" model rather than "Fischer increment". But the demand is likely to be low and introducing an option of delay in addition to increment would the add a lot of confusion in general. In other words, more harm than good.

You can search for previous discussions on the topic if you are interested in more details and arguments.