Does balanced interconnect sound beter than RCA?

Balanced lines provide imunity to noise pickup, and are of great benefit to pro sound folk who work with a tangle of long wires. Their benefits are mostly irrelevant in the home audio situation.
The higher voltage signal (4 volts vs 2) would tend to help. However, if your preamp has good output voltage capability, (most do) one can crank up the gain in the preamp, and lower the gain in the power amp, and run single-ended lines at higher voltage. I do that.

Buscis2...Lots of interesting ideas there, but I just don't think there is much relevance to home audio equipment.

Your reason #3, relating to power supply demand, does not (IMHO) have much relevance to low level (eg: preamp) circuits, where the power requirements are so small that a very modest capacitor will smooth things out. However, in a power amp there are very real benefits from running the two channels of a stereo amp out of phase. Since most of the stereo signal is common mode (mono) this evens out the draw on the plus and minus supplies. Of course, one speaker wire must be reversed to restore proper phasing at the speakers. Some amps meet their published rms power specs, both channels driven, when the drive is out of phase. This is usually in very small print, if at all.

A balanced line interconnection obviously makes it very easy to accomplish the required polarity inversion of one signal.