Ah hah! I figured it out.
It's "Four Short Novels" (ISFDB) by Joe Haldeman. Ellison narrated the audio version.
Remembrance of Things Past
Eventually it came to pass that no one ever had to die, unless they ran out of money. When you started to feel the little aches and twinges that meant your body was running down, you just got in line at Immortality, Incorporated, and handed them your credit card. As long as you had at least a million bucks—and eventually everybody did—they would reset you to whatever age you liked.
One way people made money was by swapping knowledge around. Skills could be transferred with a technology spun off from the immortality process. You could spend a few decades becoming a great concert pianist, and then put your ability up for sale. There was no shortage of people with two million dollars who would trade one million to be their village’s Van Cliburn. In the sale of your ability, you would lose it, but you could buy it back a few decades or centuries later.
In a world where there were no children—where would you put them?—he was the only infant. He was the only person with no useful skills and, eventually, the only one alive who did not have nearly a thousand years of memory.
It was inevitable that someone would see a profit in this. A consortium with a name we would translate as Blank Slate offered to “dicuth” anyone who had a certain large sum of what passed for money, and maintain them for as long as they wanted. At first people were slightly outraged, because it was a kind of sacrilege, or were slightly amused, because it was such a transparent scheme to gather what passed for wealth.
War and Peace
Eventually it came to pass that no one ever had to die, unless they wanted to, or could be talked into it. That made it very hard to fight wars, and a larger and larger part of every nation’s military budget was given over to psychological operations directed toward their own people: Dulce et decorum est just wasn’t convincing enough anymore.
Wars were all fought in Death Valley, with primitive hand weapons, and the United States grew wealthy renting the place out, until it inevitably found itself fighting a series of wars for Death Valley, during one of which O’Malley himself finally died, charging a phalanx of no-longer-immortal pikemen on his robotic horse, waving a broken sword. His final words were, famously, “Oh, shit.”
There was a worldwide referendum, utilizing something indistinguishable from telepathy, where everybody agreed to change the name of the planet to Death Valley, and on the eve of the new century, A.D. 3000, have at each other.
The Way of All Flesh
Eventually it came to pass that no one ever had to die, so long as just one person loved them. The process that provided immortality was fueled that way.
The fourth story was "Crime and Punishment", which was about criminals and the ability generate backup clones named "Farlies".
Eventually it came to pass that no one ever had to die, unless they were so horrible that society had to dispose of them. Other than the occasional horrible person, the world was in an idyllic state, everyone living as long as they wanted to, doing what they wanted to do.
This is how things got back to normal.