The lawyers and insurance companies would stop you.
This isn't a new idea, and the early satellites used a lot of gold in them. However, all those satellites have an owner, and those owners are not willing to let you take the satellites away for "recycling" without getting a profit-eliminating payment.
Clearing debris from orbit has less of a market than removing CO₂ from the atmosphere. If there was a space-debris equivalent to the Kyoto Accord, maybe they would be comparable.
I disagree. At least if you consider spent satellites to be "junk".
There's a lot of junk floating around, that is tracked, that precludes the use of certain orbits. Some of those orbits are valuable and clearing them would provide an ideal location for new satellites.
In particular, there are a limited number of geosynchronous slots -- especially those that are located over large (wealthy) landmasses. These slots are incredibly valuable.
I believe that the "good behaviour" requires satellites which inhabit these slots to retain enough fuel towards the end of their lives to move out of the slot so it can be used for a successor. However, only about a third of them do so:
Isn't this one of those "tragedy of the commons" problems, if you go up and clean it and the US gov't pays you for it, what happens when any one of the Russians, the EU, or the Chinese put a satellite in that orbit without helping pay for it?
In particular, there are a limited number of geosynchronous slots
Really? That's a circle of about 43,000 km radius, so more than 170,000 km long. Even if you want certain points, it's not like it's packed over there. You can separate a satellite some km from the next and still have plenty of space for hundreds. If a satellite is at the same distance from Earth as others, they won't be moving relative to them.
Really! The orbit of a satellite is not perfectly stable because of the effects of the solar wind, the gravitational lumpiness of the earth, etc. IIRC the slot for a satellite is about 300 mi. wide. There are preferred slots such as over Europe or the east coast of the US with lots of countries contending for them, and slots allocated to countries that don't yet have satellites.
The major junk problem is in LEO. Basically everything in geo is equatorial, so you don't have orbits intersecting at large angles, so you don't have the problem where a stray paint chip in an oblique orbit craters your sensor. Also, getting stuff to geo is way expensive, so there's less up there.