The issue is not a matter of ability, but rather a matter of cost. Raising the wrecks is most possible as evidenced by BP 's deep water efforts in the Gulf of Mexico. To raise a wreck will require, capital equipment of a rather significant amount, barges, support vessels, slings, cranes, and other associated high cost capital equipment items. Highly skilled manpower in the form of engineers, biologists, technicians such as millwrights, truckers, poteinally some divers and more critically underwater vehicle operatrors. Significant quaities most importantly of time is required adding to both the labor budget and the capital costs of the project budget. All of which will requier alot of money. One can assume, even the raising of even a modest vessel from depth would cost in the tens, if not hundreds of millions of dollars.
But all of the above is just required to bring the object to the surface. Once the vessel is on the surface the cost and the complexity really starts to get complicated and more importanly costly. With the vessel on the surface it must be preserved in a rather precise and controlled manner, otherwise the object will deteriorate before onces eyes. So now the requirement of a large temperature and humdically controlled facility to store the vessel comes into play . Transportation from the body of water to the facility is needed and associated equipment. Technicians manning and caring for the vessel on a 24/7 basis for a number of years and large quantiies of specialiized chemicals to stablilze the organic material from which the vessel was constructed.
So while the task would be difficult, exciting and dramatic to a raise a vessel to the surface, the problem is much more a matter of cost rather than techical problems. One much generally assume only a govenmental body would be interested. One last question which also needs to addressed that I will leave for others is would the information gained be worth the cost in time, energy and dollars expended?
I suggest you may wish to research the raising of the American Civil War submarine Hunley and what was required to protect that vessel once on the surface.