Why are motors above 2hp generally 240V motors?
The current gets too high for common conductors to work for large motors at 120V. The running current is not so much the issue, it is the starting current. The best 2hp induction motors have an inrush of almost 30A at startup. Fortunately it doesn't last long enough to overheat the conductor but if we went up to a 3hp motor, you can see where we are well above what a 20A circuit can safely handle. The conversion of hp to kw is almost .75kW/hp. So a 2hp motor would draw about 12.5A. So the running load of a 3hp might just squeak under 20A - but we haven't figured in effiency yet - but when we consider startup, it is clearly too much. You'd also need outlets and plugs and flexible conductors capable of the higher current. The biggest commonly available 120V outlet is 20A.
Why above 5hp generally motors are 3 phase?
I am certainly no expert in specifying large electrical motors. I checked only two sources to verify your assertion that motors above 5hp are generally 3 phase. McMaster Carr agrees with that statement, Amazon does not. I would guess there is a difference in audience that may help explain that. In a home, we are typically limited to single phase power and would thus want a motor that is single phase. In a plant, 3 phase power could be more readily available and would save wiring in the plant. But that is just a guess. Large customers sometimes get billed for power factor - kind of like electric usage by phase - and that would make them want to use 3 phase motors.
What about back EMF in the stator windings?
I don't understand the reference. All motors, even DC motors, have back EMF. I don't think it's a difference between single and 3 phase motors. Or a difference between 120V and 230V motors.
What about I squared R losses especially during motor start?
Higher current means 120V motors will have higher resistive (I squared R) losses. I wouldn't count on seeing any difference in your electric bill if you change.
What about switching and arcing when interrupting a low current circuit versus a high current circuit?
The ability to arc is created by the voltage, not the current. Higher voltage switches require more careful design and tend to be more expensive because of this.
Why is it much easier to stall a 3hp 120V router, compared to 3hp 240V shaper?
The router is not really a 3hp motor. Universal motors tend to get a rating based upon their stall current and running voltage which never occur simultaneously. I just bought a PC 7518 for my router table. It is rated 3.25 hp by the manufacturer. But it also is rated to pull 15A. If it was 100% efficient, 15A at 120V would only be 1.35hp. Universal motors are not typically really high effiency so I would guess it's closer to a 1hp router. That is still a big one. But even a 1.35 hp router would be less powerful than a 3hp shaper.