[reasonattlm]

There would still be a great shortage. The supply of donor organs is tiny.

[jack9]

No shortage is more like it. Intact cadaverous hearts are plentiful by comparison to awaiting heart transplant patients. Most heart failures are immediate and fatal, but people who have progressive failure are relatively rare. Transplant patients would conceivably be donors for the program (since most heart damage is soft tissue failure).

[astazangasta]

You could use a much broader range of donor organs, and not having to worry about matching would vastly increase the number of usable donations.