I wonder if it'd be possible to augment or replace the existing living spaces (and other spaces) on a rig. Maybe turn a rig into a hotel-on-the-water kind of thing.
The thing is: You're now effectively living on an island, albeit one that requires ongoing maintenance and other expenditures to remain seaworthy. And hope you don't have a big storm that you're very exposed to. Most people don't want to live someplace where they have to take a boat trip to go to work or the grocery store.
Some are fine with that but, guess what, you can often live on islands with a fairly low COL. There's tons of land in the US generally. It's just some specific locations of land that are expensive.
From an engineering perspective, you also can't build it up that much. When I worked on rig designs, every time we added equipment, we had to verify that the center of gravity remained within acceptable limits. You can't just build a multi-level structure atop the entire rig or it would become dangerously unstable.
They've tried floating hotels before, generally they aren't successful.
The problem with floating hotels is that they're all the disadvantages of cruise ships, mixed with the disadvantages of a hotel.
Like a cruise ship, you're still on a relatively small floating building, which limits the activities you can do, and you also have to deal with sea sickness and storms. Like a hotel you're stuck in one place, the main drawcard of cruise ships is that you're cruising between locations.
Now instead of a floating hotel, you could turn it into a little sovereign floating town for libertarians. People have proposed this and made efforts to manifest such a libertarian utopia, but have never actually succeeded.
aside from the significant engineering required, my guess is that most people who could afford to construct or live on such a structure don't actually find libertarianism that appealing.