Typically overtime pay requires approval from management

I don't think they are in a place to deny it if they are fighting a video game launch deadline.

When management needs to pay more for crunch then it will prove whether the deadline is real or fake. eg. If we don't meet this deadline will it materially affect the business... or is it not really needed and it's better to save on the overtime pay.

It aligns incentives to reduce crunch as much as is feasible

It will incentivize the management to prohibit working overtime and/or hire more people.