I'll watch coverage of anything as long as it's pretty clear that things are being told once. When "repeat info" starts to turn the coverage into little but re-hash I turn off the coverage until I think there's been time for some new information/event related to the original event turn up.
It does victims of tragedy, and anyone else experiencing the sense of sadness and loss, or us; any good for us, as individuals, to let it consume our thoughts. Taking mental rest from it all (to whatever degree anyone, with different levels of involvement in/exposure to, the tragedy can take that mental rest) helps replenish emotional energy to deal with/process things (but also "the rest of live in general").
I don't really think how a person takes that mental rest matters much (although I think "mental rest" while awake is a different, and important, thing from just going to sleep and no thinking about anything at all). Fresh air and a little conversation with someone else (about something other than the tragedy) helps most people, I think. Something else that I think is important is that anyone (no matter how close he is or isn't to the tragedy) have some "fight" against it, and think, "I'm not going to let this take more away from me than it already has."