I'm not going to repeat the excellent plot oriented answers - but its my opinion that JKR probably realized that freely available and controllable time travel can critically damage your ability to make a problem that cannot be simply resolved by the protagonist.  Magic itself has that problem too - but at least she can put limits on the magic and the fact that other characters in the story have magic too which cancels out some of the power that gives Harry & co.

This is exactly why (most) of the stories that include time travel that I can think of involve plot points to make it unpredictable or uncontrollable or simply hard to do:

- Back to the Future (1.21 gigawatts of power or it is broken)
- Dr. Who (the Tardis is broken and hard to control, and for one whole period grounded entirely)
- Star Trek (its always some accident or external issue - though magically they always get to return ok)
- The Time Tunnel (i seem to recall that there is an accident with it)
- The Time Machine (he passes out when using it and ends up going too far)