There are several good reasons for this. You're probably storing your set in the garage or an outbuilding which is, by nature, damp. When you run your set for a half hour with an electrical load on it, you give the set a chance to warm up to operating temperature and that drives out the moisture. If you don't do this, you're likely to find that your generator won't start or won't work when you need it. Moving parts are happiest when they're moving.
Moisture means corrosion and rust.
If your set worked last week, chances are it will work this week. If you try to start it under normal conditions and for some reason it won't fire up or put out the juice, you can fix it when it isn't dark and cold. Once a week, the generator automatically starts and runs for 30 minutes and then shuts down. They wouldn't do that unless there was a good reason. I would rather buy a set that I knew ran for a half-hour a week than one that sat around rusting in the box for the last year.