I'll take a crack at the questions. Modern thermostats have a delay circuit so the compressor doesn't get started until the head pressure has at least mostly bled off, so that's not the main issue. The main issue is just getting the motor spun up from a dead stop. When the motor isn't running its windings are more of a short circuit than an inductive load. The head pressure won't build until the motor builds up some speed. Low voltage will definitely damage a motor over time. The easy start device is likely out of the picture within a few seconds. Multiple people have posted the opinion that low startup voltage will over time damage the motor. I personally don't agree, but just as they can't prove the damage occurs, I can't prove it doesn't.
I assume the easy start works by chopping the AC waveform to achieve a reduced RMS voltage, just as a light dimmer does. A simple reduced voltage, as with a temporary overloaded generator, does the same thing, but chopping the waveform accomplishes the end result more gracefully and efficiently. The easy start likely has a programmed algorithm to control the waveform chopping. With no disrespect intended, I consider the description posted by the manufacturer's representative to be just marketing gobbledegook, with nice sounding words that don't say much about how it really works. The easy start web site has additional info.
The easy start concept is not new. In some Hawaii municipalities, air conditioner inrush current is limited by statute and devices similar to the easy start have been in use for years. At least one air conditioner manufacturer (Rheem) has certified that the device does not damage their air conditioners. Dometic markets a similar device for the marine market, which would probably be just fine for RV use, at marine prices of course. Looks like the easy start device mentioned in this thread is bringing the technology to the RV market at RV market prices. It would not surprise me if in the foreseeable future a device like this becomes a standard builtin feature of the air conditioners.