The benefit of not running the 24 Volt motor on 36 Volts is that it will run cooler and last longer on 24 Volts. Other than that there is nothing wrong with overvolting it to 36 Volts.
This is the first time that I have heard of a controller with over Voltage protection so this is new to me. The controller manufacturer must have done that to prevent it from being overvolted for safety or warranty purposes.
I do not have any experience with modifying controllers so I do not know if modifying it in one way or another would be right or wrong.