Right now something like 30% of the space junk up there comes from one
Chinese satellite getting into a collision. We have at the moment no workable ideas for how to get that debris down other than wait a few centuries. And since it is traveling over 10,000 miles per hour, blasting it into smithereens just results in too much sand to track, but even a single grain of the stuff is potentially lethal.
Before I'd support your approach, I'd want to see answers to how we plan to get rid of the debris from one collision. After that I'd like to see a plan to handle the potential problems from a careless company cutting corners and having a few more space accidents. And before you wave the free market magic wand, with known techniques it takes a lot of work to get a single flying screw down. How do we supply a profit motive to reward private enterprise for that work?
It is always easy to say, "Oh the market will take care of it." But markets don't work very well for certain kinds of problems, and dealing with litter in near space seems to be one of those problems.
And for the record I'd love to see a solution to it. Because until we can come up with a solution, I don't think we're going to successfully colonize near space. (The ultimate solution may be to be very, very careful with near space and instead leapfrog human colonization out of low Earth orbit.)