The second stage often does make it to orbit, where it deploys the payload and then usually becomes orbital debris. A few upper stages (falcon 9, for example) do a small engine burn to reenter the atmosphere where they burn up.
Collecting upper stages would be... hard. Every rocket is on a different trajectory. Making some vessel that could 'collect' them would have to visit every launch trajectory that they'd each taken, which is a lot of orbital maneuvering and coordination. Then the problem of docking and collecting the stages and packaging them for reentry would be a whole series of ridiculously tough engineering challenges.
The upper stage is much smaller than the first stage, so it's usually significantly cheaper than the first stage.
Basically, recovery of the upper stage is much harder than recovery of the first stage and has less upside.
This is assuming small rockets are also expensive and could save money if they could reuse them.