What is the dependance of voltages in a MOSFET on its Performance?
Capacitance.

I'll let the device physicists fill in the details, and the question is not clear whether you are interested in logic speed or power switching but since you mention scaling I'll assume the former.

Logic switching in the CMOS world is all about charging and discharging capacitors. These may be the gate capacitors of succeeding stages, or just the wiring capacitance of that signal. To charge a capacitor fast requires high current : to attain high current, you have to make the MOSFET's channel resistance low.

And you will see from any MOSFET's datasheet - including power MOSFETs - that the threshold voltage only defines the point where the MOSFET starts to turn on - with a high resistance, in the 10s or hundreds of kilohms. To turn it fully on requires several times the threshold voltage - at least twice and sometimes 4x the threshold voltage. It follows that Vdd/Vth should be 4 or so (ideally). And if you shrink the process, the maximum Vdd decreases (I used to say you can get a lot of volts/metre across a micron! and scaling has come a long way since then) so the threshold voltage must also decrease .... or learn to live with slower logic.