This used to be the case, but recent advancements in mosfets has made them more suitable for voltages up to about 1000v.
The 'high speed' bit actually translates into more efficiency, less cooling, less weight, less cost, etc.
Thats because when designing any switched mode power supply, you need to decide on a switching speed. They might range from ~8kHz (in early EV's - they make a whine) to 2Mhz+ (used in phone chargers), and can be dynamic.
Every switch loses some energy, since while the switch is mid-switch ie. 'half on', it is having huge resistive losses. You therefore want each switch to be completed as fast as possible, and to do switching as infrequently as possible.
However, switching too infrequently has downsides. For a given motor inductance, if you switch less frequently, there will be more ripple current - ie. the current flow in a motor coil will rise while the switch is on, and fall when it is off, and if you turn the switch on and off less frequently, that rise and fall will be more. Ripple current reduces efficiency, because the power delivered to the wheels is proportional to the average current, but the losses are proportional to the instantaneous current squared - so ripple wants to be minimized.
The only other way to reduce ripple current is to increase the motor inductance - but that involves more metal in the motor core (heavy, expensive), and that also has other negative performance side effects.
So, in summary, system design is about balancing the desire for high switching speed (less ripple current therefore more efficiency) with a low switching speed (fewer switches therefore fewer losses during switching). Since MOSFETS can switch faster, the losses involved with each switch are lower, so they can use a higher frequency and reduce ripple current, less iron in the motor core, less weight, less cooling in both the motor and drive electronics, and generally better all round.
Apart from cost. They cost more. But the cost is usually outweighed by the savings in all the other systems of less cooling, smaller motor core, higher efficiency therefore smaller battery, smoothing capacitors can be smaller.