They act as havens for marine life. If we had to dive out in the middle of the Gulf of Mexico, critters would be few and far between. Under a rig there are tons of critters. Granted, there are wrecks and other artificial reefs out in the Gulf, but they are much, much fewer in number than the rigs are. You'll see overfishing of certain spots, and the rigs get crowded with fishing boats as it is right now, I can only imagine if you decrease the number of available spots to fish on out there.
Most fishing is done off of either private boats or charters from here. The charters are usually one day excursions for both hook and line fishing and spearfishing. Depending on the spearfishing charter, you may hit 2-3 rigs in a day with everyone in the water at one time (my preference) or 6-10 rigs in a day with a buddy team jumping over the side, bouncing down, shooting what they can as quickly as they can, and then getting back on the boat which then moves to the next rig depending on how plentiful the fish are reported to be by the team. The next team gets ready, and they repeat all day.