Adequate torque from VFD driven motors?

Hello list

When the speed of a spindle drive motor is reduced by step or variable
diameter pulleys, the torque is multiplied by the same ratio that the
speed is reduced. In other words, lower speed - higher torque. This is
consistent with what is needed by machine tools.
But when spindle speed is reduced by reducing motor speed using a VFD,
torque is reduced in the same proportion as speed, isn't it? In other
words, lower speed - lower torque.
But VFD's have been recommended on this list, and most new commercial
CNC machines seem to control spindle speed this way. So how can this
be?
I am retrofitting a lathe that had an elaborate mechanical variable
speed drive, and it would a lot easier to go the VFD route, especially
so CSS could be implemented. But I just don't see how there could not
be a lack of power at lower speeds. What am I missing?

TIA,

Steve Clay-Young