Why are so many big milling machines 3 phase?

Its not about horsepower. I have a compressor with a 5 horse motor that
runs on 120V. It draw close to 20 amps on startup, but...

Straight single phase 220V is more than adequate for any power for most shop
machines. There are some big machines out there, but for most shop machines
its fine.

I can think of two possible answers.

1. Price of electricity. It was explained to me that power companies
often charged based on the peak demand of the leg drawing the most current
at any given time. By balancing the load you can reduce your power bill.

2. Smoother operation. With the vagaries of the power supply from many
electric companies by going 3 phase you can get a smoother operating motor
with less variance of speed.

(I have worked in facilities with 440 and even 680 motors, but that is
a-whole-nuther conversation.)