Dometic sells hard-start boosters for 120V units. They call it "soft starter" because this is what it does - softens the start current.
Inverter type 120V is better - it always starts soft, and mostly it doesn't "start" at all, only variable speed goes up and down.
12V inverter type (i.e. variable speed) is better yet, because there is no DC-AC inverter.
The cost of solar sufficient to run 5000 BTU window A/C 8 hrs a night vs generator - yes, solar will cost more and will return the investment in approximately 2 years. For most RV users it is not really about cost - even when they think it is - because the whole thing is a leisure time expenses. The problem is that many can't install a solar because don't know how and don't want to hire an installer, or don't have enough space for panels. OTH, generator they (often) already have, makes a sort of excuse.
For permanent campsite I would "think" it is about both cost and comfort, and here we come to the same old question - who really "enjoys" running his generator, especially in the night. For some people it is still a question, so I'll leave it there. Mex's situation is different in many ways.