How much breaking is done during a race? Would a KERS style motor w/ capacitor be beneficial?

It would be extremely beneficial, but nearly impossible to integrate. Motors used for cheating in cycling are usually in the seat tube or down tube, where they can invisibly interface with the bottom bracket (between the pedals) and connect to batteries elsewhere in the frame. Because bicycles have a freewheel in the rear hub (chain doesn't move while coasting/braking)*, a KERS would have to be located in the tiny rear wheel hub.

*You can of course get a non-race bike with a fixed chain, but UCI rules require use of a freewheel.

Now I kind of want to see a separate Formula E style league that allows KERS

There is no way to do this unless the motor is inside the wheel hub and that would be instantly obvious - regular hubs are super thin and wouldn't fit a motor + capacitor inside them. And you'd need to tell it you want to brake somehow.