You can't just wander into a PhD program, it's pretty competitive to get into a funded position. You're going to be up against a lot of fresh-faced undergraduates who may already have a publication under their belt. They also have a 3.8+ GPA, are in leadership positions in numerous clubs, have done study abroad and worked 3-4 different research jobs each summer of their undergraduate degree, and probably during the school year too. Thus, they know all the other lab heads (PIs) who could be their advisor, and when funding is available, they're the first ones to know to apply, and they're the most interesting for the advisor because they can be vouched for by other labs as being strong workers, or easy to train, or whatever. If you are just cold applying to labs you have no relationship with, that's harder. If you are just cold applying to a school, and just hoping to get placed in whatever lab has funding, that's even harder, and chances are you can end up working for a tyrant of a PI, which is why they have no students. Some advisors are so bad that people quit their degree, and it ruins them. This, aside from the expectation you work 40+ hours a week, you only get paid for 20 of those hours, usually around $30k/year, and you are bound to research whatever the lab you were lucky enough to get a position in is currently researching. So the next 4 years of your life could be spent on nematode gene editing or formulating lipid nanoparticles or whatever the lab is doing. You're basically never going to be able to just randomly pick a project because it interests you. Though maybe if you're doing a history PhD or something, you do exactly that. But that type of PhD is a deadend where you are competing for like the 75 jobs in the country that expect a history PhD.
All-in-all, it's not really a retirement hobby. If you're really rich and can self-fund your graduate studies, then you can probably go to all types of schools and work in all sorts of labs. A self-funded rich student would be great for most labs. Many schools will accept all types of people, but if you're not getting an acceptance letter with an offer of funding, it's basically like a rejection letter.
I've heard of people in retirement becoming a student for the healthcare benefits some schools offer though. They maintain enough credits to have the right status so they aren't paying a boatload, but can still be on a student healthcare plan that gives great benefits.