eBike: use 48v motor with 36v controller and battery

On one DIY eBike I currently have a 36v 250w rear hub kit. It’s a "cassette" version, not "freewheel". Problem is, the internal freewheel mecanism of the wheel is very damaged (still barely works for now, but at start I have to pedal before using the throttle, otherwise the freewheel doesn’t "grip", and it makes heavy noises, more and more over time…). Sellers had warned the "cassette" version is weaker then the default "freewheel" version…

So, I’m considering to just replace the wheel and see how long the new one works.

The thing is, I would like to take the opportunity to upgrade to a motor a bit more powerful. A 48v 500w would be nice, but my other eBikes are currently 36v, I would have to additionally buy 48v batteries (which would be very costly as I ride a lot and need a lot of capacity). Also I would have to manage 36v and 48v bikes and batteries, which I know is tedious. Also, 48v controllers are larger and I would have to adapt the bike. Finally, I already own a lot of spare 36v components (controllers, displays, etc) but not much 48v components.

I considered 36v 350w motor, but it wouldn’t be much of an improvement (if any…). I could also pick a 36v 500w motor, but I don’t feel 36v is suitable for 500w, 48v/500w would be a much better choice.

Thus, I thought of buying a 48v 500w wheel, and use it with my current 36v controller and batteries. The limiting part would be the controller, and I could upgrade the bike over time, first by trying a more powerful 36v controller, then by doing the switch to 48v controller and batteries.

Would it work? Am I right stating a motor with bigger voltage and wattage is simply sturdier, and can handle lower voltage and wattage just fine, the limiting part being only the controller?