I See Electromagnetic Fields!
And NO deep well injection pumps cannot be soft started. Think about hauing a 5-gallon bucket of water up 200+ feet. It needs a high Amp start.
We're talking about not having to deliver locked rotor amps while motor is at zero RPM, rather ramping up RPM more gradually.
If 3-phase it would be VFD. Grunfos makes well pumps like that. Constant current and torque at all RPM, rather than excessive current when slow.
Split-phase isn't as clean, but soft-start pulses some current to get motor turning, then ramp up to full is much less than a second. Peak current is significantly reduced compared to LRA.
Sure, if motor operates without an unloader the starting is more difficult. But with a turbine pump that allows some leakage, shouldn't be quite as bad as a piston type compressor for air or refrigeration (restarted without an unloader relieving pressure). At the least, power delivered lifting water is proportional to flow, so reduced at lower RPM but constant torque.
OK, could be because split-phase motors have low torque when stalled, need LRA to generate stronger magnetic field and get more torque. I think 3-phase motors have better stall torque. Like bicycle with 2 pedals vs. if it could have 3, one always at a decent angle.