I'm wondering if it is feasible to create an autonomous/remotely piloted Garbage Collector that would be knocking the junk down into atmosphere?
And space is very, very big. Similar problems to cleaning up the ocean. Even if someone comes up with an effective solution, now you need to launch a million of them to get the job done.
Maybe small space debris could be cleaned up by vaporizing it or pushing it around with lasers?
Performance would be sufficient, if, for a given interval of time, it would knock down at least as many pieces of junk, as there were collisions and new launches for the same period, plus some "margin"/"premium" to keep the counter going down.
Not with that attitude it ain't. :)
Any metallic or plastic bits can likely be melted down and turned into new parts. And even totally-unusable stuff - like perhaps that glove - can always be ground up and used as propellant in some sort of crude thruster (perhaps by ionizing the resulting bits of junk and pumping it out an ion engine, or perhaps by vaporizing it into various pressurized gases).
And there are plenty of abandoned satellites up there, too. If a satellite breaks down (often because of the sheer quantity of space junk pelting it every waking moment, by the way), it's not really feasible to go and repair it, so the usual approach is to wait for its orbit to eventually decay (which isn't entirely feasible in higher orbits) while possibly launching a replacement. There are likely whole satellites or significant fragments thereof ready for repurposing.
This isn't to mention the presence of things like launch stages sitting in orbit (at least one Saturn V launch stage, for example, is in a near-Earth heliocentric orbit and is tracked as if it were a near-Earth asteroid; Apollo 10's lunar ascent module is also - as far as we know - intact and in a heliocentric orbit, though its location has been unknown since 1969). That's a lot of stuff that's probably recyclable.
> it would be akin to building a car by walking a few thousand miles from your starting point and then trying to catch bullets that have been fired from a gun
IIRC, thousands (I forget the exact figure, and I'm too lazy to look it up at the moment) of grapefruit-sized-or-larger chunks of space junk are actively tracked on radar by the likes of NASA and USAF (or maybe NORAD; I forgot exactly who manages the data) in order to be able to warn the ISS and satellite operators of possible collisions. The ISS also gets pelted by golf-ball-sized-or-smaller bits of debris regularly enough that all the modules are built with whipple armor designed to withstand such constant pelting.
It's really closer to walking a few thousand miles in a world where all the air molecules are replaced by bullets. The tiny bits can likely be caught pretty easily by setting out a large, flat ablative shield to catch them with. The bigger bits are tracked on radar and can therefore be sought after specifically by a recovery craft.
When enough of the balloonlets are destroyed by collisions, you de-orbit the thing.
Obviously, a lot depends on the as-yet-unknown debris capture material. It would have to be very elastic, sticky, and UV-resistant.
If the capture material is sort of a slimy foam that can expand greatly in volume without losing cohesiveness, the inflatable support structure might not even be necessary. You launch the mother slime, then add the foaming agent in orbit. Anything that hits it either sticks to it or slows down while passing through, without generating additional debris.