But M1 designs that max out at 16GB don't have the memory to handle plenty of sample libraries, so I don't understand how a Mac Mini is supposed to be up to the job.
It's not just about raw cycles but about cached access to the samples. The biggest libraries can run up to 1TB and you'll probably have more than one. Obviously you don't keep everything in RAM at the same time, but even so - 16GB is a serious limitation for this kind of work.
And if you're using a computer instead of a synth rig you cannot afford to have problems, because any stuttering or glitching is painfully obvious and distracting in a live setting.
It also makes no business sense for a Broadway show that may be grossing $25m a year with a multi-year run to cut costs to the bone on its musical hardware. Considering the cost saving involved in replacing real players (for better or worse...) it makes far more sense to spend twice as much initially for a no-risk professional setup than to pinch pennies and risk glitches.