Yeah I am fussy as hell about my power. That's why I paid through the snot-box for a KATO 12-turn. And 990 dollars for a Woodward electronic governor. System goes beyond prime power to "Hospital" grade. The Sola whole house ferroresonant 3KW regulator is great except it eats 93 watts just sitting there doing nothing.
BUT! I have some incredibly (for me) expensive toys to protect. Electronic test equipment. If you were to connect a Macintosh tube-type receiver or amplifier to a cheap generator I would shudder. But microwaves and coffeemakers are light-years less sensitive. For your setup I would think a low-voltage cutout to be sensible.
Good fortune and happy RVing!