You are right. Three-phase needs less copper wire for the same amount of power delivery, which is the real reason everyone uses it. It needs less copper because

You are right. Three-phase needs less copper wire for the same amount of power delivery, which is the real reason everyone uses it. It needs less copper because it never has "dead time" where the copper isn't delivering power (hence the desire for constant instantaneous power). I tried to word my explanation as accurately as I could, but I had to leave out a lot of tricky details for people who aren't electrical engineers. You have to be careful not to mix up regular averages, RMS averages, and instantaneous values when you deal with AC. If you get them wrong, you come to incorrect conclusions, such as the idea that single-phase electricity has zero power. The average voltage is indeed zero, but you can't use regular averages when you calculate power delivery, only instantaneous voltage differences and currents. You get RMS averages when you integrate those instantaneous values over time, and that brings in the the cos(phi) issues you mention.