Just to clarify, I was thinking of the second case. Specifically, a robot going full speed forward which the driver slows down by cutting the throttle to 50%. If it has a 6 MiniCIM drivetrain, I get that the back current through each motor is 6V/(135mohm motor resistance + 25mohm battery/wire resistance)=37.5A and the back current coming out of the motor controller is 50% of that (because it is only flowing during the ON part of the duty cycle) or 18.75A. So the total current for 6 MiniCIMs would be 112.5A. So my “100s of amps” was too high. I’d forgotten to derate by the duty cycle. Still, I’m surprised that over 100 amps isn’t problematic.
I think the case of students pushing the robot is somewhat different. If the robot is on, but the throttle is at 0% (or in the motor controller’s deadband), then my understanding is that the current just cycles through the motor controller (brake mode) or is 0 because the motor is disconnected (coast mode). If the robot is not on, no current flows through the battery because the main breaker is open. However the back emf can provide enough voltage to turn on the RoboRIO and/or motor controllers. Still, very little current flow because they don’t need much (when the the throttle is at 0%).