It's not even close to feasible IMO. These pieces of debris are traveling many times faster than bullets and they have significant mass. They would rip aerogel

It's not even close to feasible IMO. These pieces of debris are traveling many times faster than bullets and they have significant mass. They would rip aerogel to shreds. You would need square kilometers of bulletproof armor. Imagine a project to catch all the fish in the ocean except the ocean is a million times bigger, the fish are going as fast as bullets, and every fishing trawler costs a billion dollars. And you can't sell the fish to fund it. Retrieving whole defunct satellites is possible but only one or two at a time because of the huge amount of fuel needed to match orbits with each one. And once you've grabbed one it takes even more fuel to de-orbit it (which you'll notice didn't happen here). Don't forget that every maneuver you make as a spacecraft has to use extra fuel just to haul all the fuel for every future maneuver you'll ever do, and that compounds for every lifetime maneuver. It's worthwhile to dispose of old satellites so they don't collide and produce debris clouds that are basically impossible to clean forever, but it's not funded.