I'm in California, we have a law on the books that any health care professional who has a patient meeting organ donor criteria gets called in and evaluated for donation. Generally this is:

1. A Glasgow Coma score of less than 5 (normal is 15, less than 9 generally means you need to be intubated to be kept alive.
2. the loss of 1 of more brain stem reflexes.
3. discussions of the possibility of removing life support or the futility of life support may occur, etc.
4. Any patient that dies in the hospital, gets called in for evaluation for organ/tissue donation by law.

I've taken care of many patients who have been prepped for organ donation post brain death or cardiac death in the OR.

Obtaining organs isn't an easy process. Kidneys can be obtained from a living donor. But, other organs such as the heart and lungs are very delicate and any prolonged time without tissue perfusion will make them ineligible for donation. The reason most of our donors come from events such as car accidents is because they decline so fast in the field that they are often intubated at the site of the accident or in the ER.

A good candidate for organ donation is also a very involved patient because of all the requirements with imaging, labs etc. You can't declare a person brain dead until you have rules out all other contributing factors such as electrolyte imbalances, blood gases, sedative medications, etc. When you take care of one of these patients you are on a 1:1 in them in the ICU. Doing blood work every 6 hours, x-rays, CT, cath lab and on and on, just to determine if they are even eligible for donation.

Then on the other side of things the donation team is running all of their biomarkers to determine who is an eligible match. Besides antibodies a recipient needs to be of a simular body size and age so that the organ can work properly in their body and not be in effective or too old. They also usually have to be a simular race so that their antibodies match as well. You can also find someone needing an organ that has an infectious disease such as hepatitis or HIV and still donate to that person if the donor also has that disease. Sometimes if the donor has certain diseases, but healthy organs they will still do the transplant, and then treat the recipient for that disease.

Covid was horrible though, because we had so many people die, but their organs were destroyed by the vascular damage Covid did to them that none of them could be an organ donor.

But, even if you can't get a person to be a good organ donor due to whatever they died of, many can still be tissue donors ( a better more viable option if you were to do an "opt-out" program). One person can donate enough tissue to help 90 people receive tissue grafts.