I've only ever used inverters when the engines are running, I believe, although I'm probably not correct that they ruin batteries. I'm in the electrical trade and you're a spark aren't you Roy? Getting 240v from 12v reliably seems like witchcraft to me!
We've had both and this time, due to having a smaller boat, we are trying to manage with just an inverter. Partly also because in the past, we didn't use the genny as much as I thought we would. It always seemed a bit wasteful running a diesel genny just to charge batteries, or for ten minutes to run the George Foreman.
To help matters we have x3 house batteries about 140ah each, and we are just about to instal a diesel water heater.
Using the inverter to run the immersion in the calorifier flattens the batteries too quickly.
Individually, we run a microwave, a George Foreman, coffee machine on ac through the inverter.
It's easier when we do plug into shore power but the inverter is adequate for our needs otherwise. I'm sure 10 mins of hair drying would be fine, but half an hour of the calorifier reduces our batteries by about 25-30% which is too much to easily get back into them through charge from the engines, if anchored for a few days.
Roy I have both. I have disconnected the inverter. Fine for the tv for short periods but admirals and kids just dont get it. Run the microwave and the tv. Put the kettle on. You spend your life resetting the inverter trip switch and then running the genny to recharge the batteries. Most deep cycle batteries cannot service the demand placed by an inverter for long resulting in a voltage drop. Bing, bloody inverter cuts out, batteries back to 13.7 Volts. I'm not saying they dont have their place, but if you want to keep admiral happy. Get a genny first, an inverter second. Oh, and my inverter is only 1000W. Not enough for hairdryers but plenty nuff to beggar the batteries. Now I keep the inverter just in case I need to run a lappy or sensitive electronics that need pure sinewave. 3kw Honda genny for everything else. Which isnt much tbh. Ive gone completely 12 volts. TV blue ray the lot.
As you said yourself - its for rare occasions, so a genny would be waste of money.
During my summerholiday I spent only 5 nights in a Marina but 20 nights at anchor, using the inverter every day, though not for cooking.
Should the batteries not cope with the hairdryer, then simply start engine while hairdryer is in use.