just interested in why they have to wait for a slow cumbersome ship to arrive
Slow and cumbersome compared to what? Are you thinking of flying divers to the ships on site by chopper? They might do that if they had qualified military divers but I can't see some admiral saying, "a TDI rebreather C-card will be fine".
am i over simplifying it?
Probably. Bureaucracies are very reluctant to use non-professionals for any potentially dangerous task. The risk to the decision-maker's career is enormous if they add civilian amature divers to the body count. I have no doubt that plenty of tech divers would volunteer for the task but the best they could hope to accomplish is find the wreck/coffin. Anyone alive would be hammering SOS on the hull which any number of ASW (Anti-submarine Warfare) vessels and aircraft searching the area could detect from many miles away.