If the engine uses steel or iron parts lubed with oil, you should run it from time to time for no other reason than to scrape the rust off before it welds things together so they can’t move.
The manual for one of my generators has a section mentioning what to do if it hasn’t been run in a long enough time to where the field coils have lost their residual magnetism so they can’t get the current started. It involves shorting a battery across some terminals briefly. That sounded exciting enough to me that I determined to avoid the issue entirely and just run the thing for a half hour every month or so. For what it’s worth, that generator is only 3 or 4 years old.
