In addition to what others said, if you know or suspect the procedure is extremely risky, and no other good options exist, you _do_ start with the least healthy.

As an example, the patient who got the first heart transplant:

“As a result of heart attacks in 1965, approximately only one third of his heart was still functioning. In late October, he went into a diabetic coma, but regained consciousness. […] He was also suffering from kidney and liver failure.”

(https://en.wikipedia.org/wiki/Louis_Washkansky)