Well having a closed ecosystem surely does change colors some how. But I think one reason you don't see those colors in the wild is quite frankly the lighting, we do a poor job at reproducing natural sunlight in any type of accuracy. Sure you might argue that deeper waters are more blue or what not, but qute frankly 20kK bulbs does not mimic natural light at ANY depth, ditto with actinic lighting, yes those wavelengths do exist in natural sunlight but there's so much other that overwhelms those little 420nm areas.
Now that was just the lighting to get the colors that really "pop". I think the other side is that brown is just what happens in nature, I've read that in some areas over 99% of the corals are brown or other dull variations (that doesn't mean they're doing bad either), now if that's the norm, then we basically get a small fraction of what's out there.
Anyways I'm sure there are other reasons, but if I had to put money on "brightness" I'd have to say our lights artificially make corals look that way. Two tests to get this hypothesis, 1) turn your tank lights out and have regular room lights on, do your corals look as vibrant? 2) if you can remove a particular colorful frag from the tank and bring it outside in the sunlight to see if it still pops.