You are asking the wrong question, and everybody is giving the wrong answer without realizing they are answering the wrong question.
You need to be asking: How quick does the current measurement and the overcurrent reaction circuit/software need to be? The answer is not the switching frequency, but a certain time in nano or microseconds -- time from the current level rising near to causing issues (blown parts, or even just functional issues such as control loop stability going out of designed bounds) to when the FETs actually turn off, and will tell you the bandwidth needed for the current sense amplifier, the comparator speed required, synchronization delays to any digital part, worst case interrupt latency in the MCU if the protection goes through software (usually not), etc.
All of this happens completely separate from any switching.
Switching frequency is mostly irrelevant in the context of "current rising too fast", causing saturation and blown FETs.
Current rise depends on the DC bus voltage and the motor inductance.
Increasing the switching freq doesn't magically make the "fast rising current" issue go away, it's still rising fast (during the active cycles; the duty cycle of which is hard to guarantee in corner cases) and you still need to measure it quickly enough and react in time.
Similarly, low switching freq doesn't magically make the "fast rising current" problem worse; you should have an overcurrent trip circuit that can terminate any single PWM cycle midway, which is almost always the case, because:
The current control is separate from the PWM generation!
Quick current sensing and "pulse by pulse limiting" is basics 101 in any inverter / motor drive, and the only way to go. Practically all relevant drive ICs, including MCU timers, include support for this (for example: most motor control MCUs offer an analog comparator directly routable to a "timer break input", which instantly resets the timer output, regardless of whats going on in the PWM value).
Although, it doesn't always need to actually be "pulse by pulse"; it just needs to be fast enough. Sometimes, the required time is less than one PWM period, sometimes it's more. It is extremely easy to calculate from di/dt = V/L, and the switching frequency is not a part of the equation.