I actually think the OP's question is a very interesting one. Of course it doesn't make sense to do a lot of mattress runs to get access to a few treadmills, but I think one of the hotel systems could certainly eke out a competitive advantage by giving some non-stay rights to their top elites. The difficult part for them is not giving too much away. For example, if you give rights to the lounges, a Hilton Diamond Elite living near the Arch de Triumpe could probably never have to pay for another meal. However, maybe up to 10 non-stay lounge visits per year for an elite would be nice.

As to the gym, I bet an elite would be able to convince the front desk to make an exception fairly often if it is a one-time thing on the road. I had an hour to kill in Florida once and walked into a Starwood or Hilton limited service hotel with a small, but nice, gym, told them I was an elite and asked if they didn't mind me using their gym for an hour. A key card was in my hand before I could even fish my elite card or id out of my wallet. I would, however, recommend the hotel loyalty programs formalize this. Up to x visits?