No, it's about the safety of the blood supply. It's a weird quirk of human psychology and economics that paying for donations means fewer healthy people and more people with infectious diseases donate when it's fee-for-blood.
If you were designing based on consequences, would covering basic expenses for rare blood donors result in so many people signing up with infectious diseases that it exceeds the deaths from the Rube Goldberg scheme described in OP which limps along with just a few rare blood donors?
For an example of that, HIV likely crossed into the US from Haiti via the blood trade[0][1] which acted as both amplifier and transport after haitians had to leave DRC, and some got infected in the time they spent there.
However, that effect does not extend to many kinds of gifts. Which is why I receive some stuffed animal or similar every 10th donation (I politely refuse them, not to add to the waste in the world).
People with rare blood could be gifted things like emergency taxi rides without adverse consequences and it's just bureaucracy, not science, that is in the way.
