Maybe in the US it does, but here it definitely does not. Possibly because we use an earth leakage system with three cables for AC. Earth leakage is much safer - almost all electrocutions have the ground as the return part of the circuit so an earth leakage system means those are virtually impossible. The US I understand uses fuse boxes but we use circuit-breakers and earth leakage. On the other hand, our home power is twice the voltage of US systems so that is probably what justifies using more expensive safety systems - the risk when you get shocked is much higher at 220V.
The US has used circuit breakers for decades. You may be thinking of "earth leakage circuit breakers" (ELCB) but those are pretty obsolete at this point. Current US code requires ground fault circuit interrupters (GFCI) extensively, which are equivalent to the residual current devices (RCD) which replaced ELCBs and have been required for quite some time in most countries, regardless of how the circuits are wired. (And arc fault circuit interrupters (AFCI) are increasingly required in habitable locations.)
None of that has anything to do with power distribution. In the US (and most places) AC is typically distributed multi-wire. Single wire is used in very isolated areas (especially, e.g., Australia). Single wire in the context of this thread refers to distribution, not household service. (Pretty much every place in the world now uses a hot/neutral/ground scheme for lighting service, with additional phases possibly utilized for high-power applications.) The economics of AC vs DC for long distance transmission have more to do with power loss and equipment costs than number of conductors.