And why would they not? do they have to feel they ain’t got it anymore because age?
You can absolutely take pride in having raised your own cows. But the guy down the street can also take pride in having cooked his own steak. In fact, the guy down the street might actually be a better chef than you, even though you know how to breed cattle.
In this analogy, The guy down the street didn't cook his own steak. He told someone else to cook the steak. And then claimed that he himself cooked it. Telling himself, "wow, I'm a great chef!". When In fact, he did not cook the steak.
Your greatness as a chef isn't measured by how well you manage restaurant kitchens. That would be a great manager. Your greatness as a chef is measured by actually cooking yourself. Claiming other chef's work as your own would be dishonest and self-deception.
You get judged on the final end product, the full dining hospitality experience, as had by influential customers on a random night (like Michelin inspectors).
The food is just one factor of that experience, and the overwhelming majority of that food on any given night is not actually prepared by the chef with their name on the door, but by his/her staff (the AI Agents in this analogy).