Everyone rides the time trial.
Consider it as a normal stage, but instead of everybody starting together, they need to start alone with intervals
The difference is that there is no potential "to benefit" of riding in the bulk of the peloton (using lesser energy) during the time trial. It's every man for himself.
This discipline has it's specialists that go for the stage win, while team leaders (i.e. people going for the GC) try just to gain (or loose as little) time versus their GC opponents
Depending on how much climbs the TT has or how far away in the 3-weeks it is (the later it is, the better suited for GC-guys with more recuperation), the GC-guys can also go for the stage win, however this isn't their main objective