Making a device truly wireless

I’m investigating how feasible it might be to make a game controller truly wireless- as in I can plonk it down on a QI charging pad and that’ll power it. There seems to be plenty of options and tutorials online about making phones wireless in this way but nothing about any other kind of device.

The game controller (though probably irrelevant at this stage of enquiry) is a force feedback steering wheel and requires 12v 1.3a so, from my initial googlings, it seems there are QI pads capable of supplying enough charge at least. The plan would then be to wire a charging coil to the appropriate power connector for my device, plug that into it and stick it on the device’s underside.

Unfortunately, I know pretty much nothing about electronics or voltage and charge so appreciate there may be some pretty glaring gotcha as to why this can’t be done. Does anyone have any thoughts about why this might not be possible?