I have diesel powered heavy equipment that often sit for a year+ and put fresh batteries in and they start right up... one dozer is only 45 years old. I agree tires last longer if exercised. The three months snowbirding is usually the longest my DP sits and on the day before I plan to leave I crank it up for the first time and let the coach air up. There is lots of farm equipment that sit for 4-5 months in the winter... many 40+ years old.
I have a portable welder that sits outside, often so long between uses that the magnetism collapses and it will not weld. Spark the leads to a 12V battery and it's good to go. It was probably 20 years old when I bought it 40 years ago. Do you think I exercise my generator every 30 days?
I guess if you have nothing better to do, then taking your rig out for a 20 mile trip running the generator is not going to hurt anything, but just cranking them up will. Different strokes for different folks.