Not a diver but can understand the difficulties in 3+ knot currents. What is puzzling me, despite the constant droning of the media over how swift these underwater currents are, we are treated with video (like the one graciously posted lower last page) that appears to show the opposite. Divers meticulously poring over the tail section, with silt in the flashlight beams not really moving much at all, their exhausted gases rising vertically, and normal breathing ... in a nutshell it appears to be more similar to a training dive in a pool somewhere. What gives?
Sites that are subject to strong currents are usually dived at slack tide - when the tide is changing direction - this period may only be minutes in duration. I'm not familiar with tides/currents in the crash site area but I'd hazard a guess that slack time is a limiting factor here. As has been stated before, complex recovery operations in 3-5 knots is not really viable.