I would argue it does play a big role, especially because of "battery sag", that is significantly lowered or delayed with higher voltage. But nobody talks about that on ebikes...but everybody know when the last 10% to 15% disappear in thin air within a few pedal strokes.
Yes you are right 20A is the max for these systems, but with a higher voltage it is possible to achieve two things, better efficiency(less heat loss) and/or higher peak power with the same amount of current.
Max phase currents are controlled by the software/firmware of the controller.
The manufacturer can now cap the max current at 15A(25% reduction) and achieve the same power levels.
It makes sense for emtbs as there is a lot of intense and not constant current draw, which is pretty hard on the whole system.
If I look at it the other way, I ride eskate...the difference in efficiency and power delivery between a 42V system to a 54V is massive.
Electric sports cars are also using higher(800V) voltage systems than most of the ordinary(400V) e-cars...wonder why...efficiency and stable power delivery throughout the battery range(less battery sag).
Anyway everyone is allowed to have their own opinion...so take this as good conversation