If the rectified DC voltage is, for example, 320V, and the load (say, a PFC boost controller, for example) goes into Under-Voltage Lockout at, say, 80V, then the quick discharging of the caps stop at 80V, the capacitor voltage stays there for long enough to the NTC cool down, and if the supply is re-plugged while the NTC is still hot, the inrush current is 80V/320V = 25% less than it would be to empty capacitor bank. Not a big difference, but at least some limitation...
Add the hot resistance of the NTC, and it limits the inrush current even if it's still hot, compared to not using one at all.
This hot resistance, obviously, adds power loss and heating all the time is device is on, which totally sucks. So you need to think how to thermally insulate the NTC so it keeps hot at lower power, and not destroy nearby electrolytic capacitors.