That is in fact not true. Plenty of retirees seek out job-like things. I have a couple of examples.
A small one is my dad. He was a software developer, but thanks to Y2K consulting, he made bank and retired early. After, he spent half the year in Mexico. One of the friends he made there was a teacher. My dad ended up volunteering in the school. He had a part-time-job-like schedule and did teacher's aide things. He loved it.
On a bigger scale: In Michigan there is an arcade chain, Pinball Pete's. It was founded by Tim Arnold in 1976. I grew up there gave them a lot of quarters over years. He sold it in 1990 and retired to Las Vegas, bringing his extensive collection of arcade machines.
For a while he was doing an open house; once a month he'd let people in to play some of his collection. By 2009, he had started the Pinball Hall of Fame, a nonprofit arcade. A couple years back they moved to the Strip and expanded significantly. I was there recently and he spends hours a day there. Opening up. Collecting the quarters. Fixing machines. Telling kids to stop running.
The guy is circa 70 and he can do whatever he wants. What he wants to do is work at an arcade. He'll keep doing it until he dies.