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To slow down a car while speeding up a flywheel requires an infinitely variable gearbox. Ie. When you first start deceleration and the flywheel is stationary, you'd ideally have infinity:1 ratio. When the car is pretty much stopped, and the flywheel going fast, you'd use 1: infinity. And in between you'd use every other ratio.

Such gearboxes aren't really a thing (at least not without massive caveats).

The best you can do is fixed gear ratios and a clutch, or a CVT and a clutch to handle the ends of the range.

Both are mechanically complex and not very efficient (a typical shift under load with a clutch wastes half the energy into heat in the clutch material).

Compare to electric, where a 'gearbox' consists of software/inductors/capacitors/switches, and you can effectively have an infinite ratio (software) gearbox.

I think it is more efficient if you need power conversion i.e. gear shifting.

I think it works better with having a spinning mass in a low friction environment you want to couple and uncouple with at high speeds.