I don't go to the gym either but know several people who do and the equipment lets you strength train with a lot more weight than your body weight if that's what you're going for. You can use water jugs and stuff at home but that can be janky and potentially dangerous.
Also there's probably something to be said about traveling to a dedicated location for your workout to help you get out of the house, in the right mindset, etc. I'm sure it's similar to how some people love working from home while others prefer to go to the office to help focus better and socialize.
I'm not sure how relevant it is to compare public land in Utah against the smallest state in the nation, Rhode Island. Most of Utah is 'unihabitable' desert just like Nevada and Arizona which is why so much land can be undeveloped, another aspect states like RI don't have to contend with.