I never store my MH on the jacks. I don't think storing on just the tires does any harm - hasn't in four years so far.
I'd prefer not to have all that weight just sitting there on the hydraulic system for long periods of time. Yes, I realize that when a snow bird goes some place for the winter, they'll often sit there on their jacks for 4 - 6 months at a time without any harm - but that's my preference. Sort of a Ford and Chevy thing.......
Bill