I would not run my tank without it. Especially when considering many people keep "garden" style reefs w/ corals that normally would not be so close together in the wild-let alone the diminished water capacity in an aquarium. For example, soft corals(Sinularia, etc.) are notorious for emitting chemicals into the water column that are toxic to other soft and/or stony corals-especially SPS's. I've noticed that when I don't use GAC for a short period my skimmer starts producing more skimmate, and the water clarity declines. GAC, regular PWC's, along w/ a good skimmer, and you will be much better off.
AFAIK, from what I've read, GAC depleting trace elements is a non-issue. If it does absorb any, the amount is negligible. Most experienced hobbiest agree GAC is a good thing regardless of whether you have a reef, FO, or FOWLR.