Wayne, the problem with VFDs on something like a lathe, is that you can certainly slow down the spindle to almost zero speed, but the torque is just not there when you do so.

With a gearbox, slower speeds mean greater gear reduction and more torque multiplication. If you are swinging a really big job, and taking really heavy cuts, you need that extra drive torque that only the gearbox can provide.

A VFD will provide constant torque with constant motor current down to almost zero speed. That means available horsepower decreases with rpm. But constant torque down at very slow speed is usually not enough. You really need INCREASING torque with decreasing speed with a lathe.

A VFD on a lathe would be like driving around in only top gear in your car. While it "could" be driven around at very slow road speeds, the performance would be very poor. You really do need that gearbox in both lathe and car for exactly the same reasons.