Inverters let you program in voltage, frequency and current. Inverters give you great control over things such as motor speed, startup current, and braking. However, because the electrical parameters are digital, they can go from 0%-200% almost instantaneously, which causes electrical spikes and harmonics. This is harder on both the motor wiring, which needs better insulation, and may require modified winding techniques, as well as better designed rotors and stators to handle the harmonics. So, while inverters can be paired with "any old motor", the motor may not last as long depending upon how the inverter is programmed and used. Ideally, an inverter is always used with an inverter rated motor. In an ideal world, the inverter is close to the motor (as in inches to tens of inches), as wire length alone will affect the harmonics, which can be reduced with filters, and better inverters. The motor itself is an inductor, and will have its own particular resonance.
The advantages of an inverter on a well include things like soft start/stop, lower starting current, avoiding startup and shutdown water hammer, and reducing the torque on plumbing. However, as far as I know, there aren't many inverter rated down well pump motors, which is why I think that they aren't generally recommended. On the surface, inverter driven pumps are used in factories routinely for their ability to exactly match output with demand, minimizing energy consumption and product losses.
It is that ability to exactly match supply with demand at minimum energy that has caused such high penetration into the HVAC market, where cooling and heating is rarely 100%, and thus being able to throttle the refrigerant by adjusting the compressor motor speed gives exactly the right amount of cooling at the minimum amount of energy.
I think that home water use is too intermittent to benefit much from a just it time water flow, though Grundfos sells a pump with a tiny pressure chamber that adjusts flow to meet demand, without a big pressure tank, and with a more even pressure level.
All the best,
Peter