That is a fair question Dan.
The reasons that I can think of off the top of my head are:
Smoother surface finishes.
Infinitely adjustable spindle speeds.
*
Soft starts.
*
Spindle
braking. *
Instant spindle reversal.
* (With a VFD.)
3 phase motors run much more smoothly than single phase motors resulting in less vibration and better finishes. Switching gear levers is fine unless the speed you need falls
in between the speeds available from the two closest gear positions. And being able to run the lathe
below it's minimum "low gear" speed can be a real blessing when it comes to threading to a shoulder on a lathe if you don't have lightning reflexes. (I am in that group...)
The ramp up function of a VFD takes a lot of stress off of the machine when starting the spindle. Spinning up a heavy piece of stock instantly to 1500 RPM from a dead stop can get.... interesting. Slowly accelerating that mass up to full speed is a lot more comfortable for both the lathe and the operator.
Likewise being able to ramp
down the speed or inject additional braking, keeps the chuck from spinning forever due to the momentum when the machine is turned off.
What else did I miss guys?
Obligatory pics of my lathe....