Can't they just intubate and keep organs oxygenated and harvest really fast?
So there are a couple of variables.
Some organs last longer than others. Intestines tolerate almost no time after death, and in fact almost no time between donor and recepient despite preservation. Kidneys can tolerate a short bit, but not more than an hour or so and typically we find that the kidney is too damaged by the time it gets to us for implantation. Lungs, hearts, and livers can tolerate a bit longer between harvesting and implanting, but are still very sensitive to time between death and harvest.
Patients with large open trauma are at large risk for infection, it makes donation dicey even with large amounts of antibiotics, keep in mind that if you are looking at kidneys most antibiotics are nephrotoxic to varying degrees.
You need to match the patient to the organ. For solid organs that are end stage disease (mostly livers) we typically are good with just an aborh match but electives we are much more choosy (in fact we can do aborh mismatched livers, but then we also can do living donor pretty often so it isn't as big of a gain).
You need good end organ perfusion before you harvest. We want that organ to be as good as it can, because it is the best it will ever be for the recipient. The day we put in a solid organ is the day the body starts to fight it and scar it. Any hit from inadequate perfusion prior to harvest is a huge deal. We have had recipients on table, lined, and anesthetized only to have to recover them without transplant because the organ that showed up just wasn't good enough.
Typically a donor who has had a large anoxic hit who is pronounced brain dead will provide the best donor organs. The OPO team will wean any pressors they can to increase perfusion to the harvested organs, often instead titrating things like synthroid drips.
Traumas are also likely to receive unmatched blood. In most systems that means that women who are older than child bearing age and males over 18 may receive O+ for their first 2 units of PRBCs or fresh whole blood. Since the patient essentially now has the potential to have a different blood type than when they were first typed deciding matches can be difficult, it can take 3 days for a follow up typing to accuratly show what antibodies the patient now has. With this keep in mind that in addition to ABO and RH there are 28 other blood group systems that can be typed, while this typically would have little effect in blood donation it can make a huge difference for organs.