Here is a good article that covers a lot of things (that ironically just came to our email).
https://blog.rvtrader.com/2020/11/fm...e-dos-and.html
The reason for starting and running gas powered engines (and the article refers to this for the generator) is to prevent/minimize gumming up of gasoline. The manufacturer of our generator recommends running at least once a month at full load (thus using the A/C unit).
We have a few classic muscle cars that we also run once a month while stored in our garage. We take them to operating temp and cycle through the gears (automatics) a few times to help lubricate the seals. I can tell you that if we DON'T do this, seals will harden and eventually leak over time. I know this from experience and thank goodness mechanic friends reinforced this with me after the first time it happened years ago. I would think a gas powered RV would fall under the same recommendations.
We also move our rigs 6 to 12" once a month to minimize flat spots on our tires. I've never had an issue with it, but maybe because we do this with all of our stored vehicles. The article also mentions this.
Bottom line is do what you are comfortable with. This topic of running the generator and the MH engine has been debated many times on these forums. There are sound points on both sides of the issue. I just know that after the expense of replacing transmission seals and rear main on a classic car, I won't take the chance of that happening again...and it hasn't after I took the mechanics' recommendation. But then again, I'm not the lucky one at the casinos...my wife is! (That's meant as a joke...)
Al