I don't know much about motor control, is it normal to need that fast of feedback?
Fast feedback loops are also necessary in SMPS, another area where precision, low latency MCU peripherals and software are actively displacing traditional approaches.
I’ll see myself out of the Internet now.
If the sensor has a limited bandwidth, you add the conversion delay and then the computation delay on top of that you end up with a max workable loop bandwidth in the low tens of kHz and anything higher will have overshoots, oscillations, etc.
If one is trying to do some assembly line (max # of operations per second), the power requirements alone get hard to manage. And then you're managing back EMF, eddy currents, heck, air resistance!
My rule: have dedicated low-level hw provide smooth PID response, mostly on the P term; and have a higher-level control produce the setpoint. Faster response means less need to rely on I or D terms as much (just because delta-T is so relatively small).
It's not that important if you use current sensors on the motor phases. But then you're looking at HALL sensors or a shunt with a very high gain amplifier with good common mode rejection - looking for mV signals on top of a +12V or +48V square wave at PWM frequency.
By using low-side shunts under each half-bridge you don't need the common mode rejection, but you can only measure phase current while the low side FET for that phase is on. That means limiting the PWM duty cycle to ensure that FET is on long enough to measure current, so we trade available voltage range for sample time.
I've also written code to measure all phase voltages with a single low-side current shunt under the whole 3-phase bridge. That requires careful phase shifting of the PWM signals and very fast conversion time, but you don't have to compromise available voltage range 0-100 percent duty cycle is possible.
Typically we run the control loop at PWM frequency, but the measurements need to be faster than that.