I've taken apart several of these kids' power cars that have been left in the alley for bulk trash collection when their batteries die. Useful for some of the wiring and contacts and switches. Motors if you need them for small powerdrills/etc.
There are no controllers; it's on or off, just a 12V 6Ah SLA under a plastic cover, and some rocker switches under "clever" plastic lever covers that switch +/- to the motors for reverse, and another rocker switch under the "accelerator".
There was one that had a two-position rocker under the pedal, and it had two 12v batteries. That rocker switched it off, or 12v parallel, or 24v series. All of the contacts on that switch were blue from overheating, and the plastic of the switch casing and rocker were distorted; the switch would not move.
The only ohter electrical parts were what I think was a PTC self-resetting fuse in series with the battery, and the small motors themselves, one to each rear wheel. Just little brushed motors, about the same size as what's in my smaller Ryobi weedeater that I burned up with a 3s2p RC LiPo pack, replacing it's 12v 6Ah SLA.
My guess based on my experience with that Ryobi is that using a higher voltage on that motor is going to greatly increase the heat load, and even just using a "stiffer" battery that doesn't sag as much at just the original voltage, total power in the motors would be enough higher to overheat them pretty quickly.