Yes, that is a good point about the the battery management system. If the battery has a low voltage cutoff (LVC), that will also shut the battery down at its minimum voltage, but some batteries may not have an LVC, or it may be an older design with one that don't work so good. I have been fooling around with some batteries that don't have an LV alarm. Well they do. They will light up an LED if the battery is in the undercharge zone, which I cannot see with the batteries in a bag behind me. So I trust the controller will shut down if they get really low. As far as battery quiality, I also bought a not so cheap battery from a US vendor, and its USB port was fake. I think we users ought to take some care.

I also have a 36 volt controller that powers up and spins my motor on a 48 volt battery, but its capacitors are rated for 50 volts. A 48 volt battery is really 54 volts at full charge. Would not be good for long term reliability to over volt that controller.

You guys can do what you want, but I think a newbie user should follow specifciations I wouldn't mind melting a $30 controller, but even cheap batteries are several hundred bucks. Don't want to ruin one of them.

The other thing for the OP to look at is the voltage rating on his charger. If he doesn't want to buy a new charger, he can save 30 bucks by getting the same size battery as the charger rating.