I too had a boss in his 80s who was the patriarch of the company, he had one son who was a partner when I was there. By staying involved, he could live like gentry alongside his clients, going on interesting trips, and participating in interesting ventures, and being invited to many parties to mingle with the local high status. I don't think pouring his own nest egg into similar ventures would be the same. It was the difference between upper class rich and middle class rich.
His son developed his own upper-class tastes but had no interest in mingling business and pleasure. He had an interest in making international big game hunting trips frequently. Whereas the father's extracurriculars always involved the business, generating leads, etc.; his adult son's extracurriculars were just burning money as a demonstration of status.
Those are the two reasons why he would not step away.
That job was insightful but also depressing because I could recognize my own inadequacy. I want to go home after an 8 hour workday. Not a calendar of dinner with one city council member a week, a second dinner per week with a bank president or similar ilk, going to lunch with various other people, outings, parties, hearings, conferences, etc. It's both exhausting and anxiety-inducing cause of FOMO. I'm sure that's a third reason of why he would not step down.