If some of the content has already been covered, please forgive. That is an awful lot of reading for a Sunday, even if it is an electrifying subject.
Out in the boonies in Wisconsin, our electric service is single phase. Two wires can only supply a single phase. The nearest three phase lines are about five miles away. They are only routed where there is enough demand to justify running the additional wire.
Three phase generation from a a single phase can only be done in one of three ways: A static phase convereter using reactance (capacitance and/or inductance) to electrically shift the phase, a rotary phase converter where secondary windings on a motor are physically positioned 120º and 240º from the primary winding, and using a VFD to create three new phases 120º apart. I suppose using single phase to drive a motor driving a three phase generator would be a fourth.
An excellent reason for 120/240 is efficiency. On the standard 120-0-120 feed, the most tcurrent the neutral will ever carry is the larger curren of the two legs as the neutral current is the difference between the currents in each leg because they are 180º out of phase. It is the reason that we can use a 12-3 cable instead of a 12-12-8, If two equivalent lines that were in phase, an additional wire would be required.
The same is true for three phase. The current through a wire will be the vector sum of the currents in the two connected circuits. Because of the 120º phase shift, it will be less than the current in either circuit.
Add to that, that three phase is better for converting to d.c. With full wave rectification, there are six peaks per cycle instead of two. The peaks are 2.7 msec. apart rather than 8.3msec. for single phase full wave rectification which means better voltage regulation and lower cost filtering. Modern automotive alternators are three phase generators using full wave rectification.