Without knowing what you exactly looking for, but have an idea (individual PoE) I would NOT do it in the way you asked.
IF you consider some sort of PoE for devices that are kind of "energy hungry", your first thought in principle is right: the higher the Voltage, the lower the current on wire, the lower the voltage loss on the cable (you will not see anything close to 12V at the end if you input 12V and having a 100ft cable).
That's (and staying in the "safe voltage region) why they use 36 / 48V for PoE. It allows for enough loss on the cable with still enough input Voltage to make a step down regulator do the propper job for your application. You should also consider this path.
120V AC directly on a cat cable is defo out of specification and could cause significant trouble from a law and responability side! Keep in mind that not only the specification of a cable counts, also the usecase and the surrounding! In many countries, you will not be allowed to use a 120V AC cable sitting directly attached to a PELV using cable.