Originally power distribution was done with DC voltage, and the substation in the street provided 100VDC on 2 power rails from motor generators running either on steam or from a higher voltage DC supply fed in from a larger power station. Thus one side had +100V and another -100V as a supply, with higher loads being supplied by using the 2 100V lines to give 200VDC as power. The wiring was done to reduce the size of the common conductor, as it normally only has to handle the imbalance current between houses, not the whole street load, which are handled by the 2 line wires, at half the current.
When AC was being introduced, the motor generator sets were replaced by transformers and mercury arc rectifiers, still keeping the 2 power rails so as not to have to replace all the infrastructure in a district when upgrading. When finally the switch was made to AC distribution the mercury arc rectifiers were simply removed and the transformers were simply switched to supply the power rails, as all these substations either had 3 sets of gear if they had a 3 phase supply, or had 2 sets if single phase. The load output was simply rearranged to use a single phase, as again it was desired to not have to rewire the streets and houses, with the AC voltage being chosen to work with older equipment in houses at the time.
Thus the 2 phase is cast in stone. In the UK and elsewhere they had chosen a higher voltage in the beginning, typically 200-250VDC and had thus only a single wire pair along the street, as the insulation of the time was problematic at higher voltages, and winding the motors and transformers for higher voltage was more difficult, so they just supplied full current ( same current as the US on the lines as well, but capable of higher power to loads) to the lines. When they changed to AC it was merely a wiring change.