> it's not just raw material floating around
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.