Low-voltage heating cables

I may be wrong about this but I was under the impression that the reason low
volgates are used for heating cables is that wires tend to waste more
electricity to heat a wattage W when voltage V is lower than at the same
wattage W when another voltage V1 is higher.

I assumed this meant that resistance across a wire builds up as a function of
the amperage across the wire (hence, the reason fuses are labeled in amps
rather than a wattage, voltage combination).

If this is true, a low voltage heating cable would seem to me to be more
efficient at converting electrical energy into heat if you drop the voltage.

Please correct me if I'm missing something.

David Webb, getting ready to fly to Camden NJ for the FishRoom convention.