Want something valuable? Mine an asteroid for platinum, build fuel cells out of it, and undercut the terrestrial competition while cleaning up on the profit. Right there you've identified a competitive advantage (low-cost of scarce resources) to satisfy a growing market which exists today.
Last but not least, suppose that you would grant any spaceship landing in Mars the right to own all land within 250 miles. Sounds great, but why wouldn't they explore and mine the entire planet if they could?!? It's not like you have CCTV cameras on Mars to know what they're doing, where they're mining, etc. Hence, in a way that's a false incentive.
As far as companies mining the entire planet, sure they could, but they'd be poachers. The 250 mile area claim would have legal rights of ownership backed by earth governments.
The rule would obviously need to add some extra provisions to drive innovation. I dunno, require colonies within 100 years, or trips every decade to show the flag etc.
There is a reason that pretty much every single explorer on earth was financially backed by either a company or a gov't grant.