I've never even thought about conflict of interest - my mother was a teacher in the Catholic school system and I went to a public high school, so I don't think so.
I have always tried to be a good sister and encourage my brother. I wanted him to go to college because he is brilliant especially with computers, but he never went. My mother discouraged him by refusing to help pay, although she and my father both had degrees (my mother is British so her education was free). I took out student loans for my degree, but my brother didn't want to and his future wife wasn't in favour of him getting into debt. He really regrets it now.

I have suggested he go back but he refuses. He worked for a small company for years in the warehouse and then when he got laid off spent a few years doing deliveries for Amazon. They are pretty well off financially though because his wife is a book-keeper and his best friend from high school is a hotshot investment advisor so they have made a lot of money on the stock market. Also my brother had Critical Illness Insurance so got a large lump sum from his cancer diagnosis. But he refuses to spend any of it on getting any more education for himself. His 19-year-old son is in college and they are saving to buy him his own condo. I wish my brother would spend a little money on himself. My personal feeling is he has no hope left for himself and just wants to pour everything into his son. I'm going to perhaps have a chat with my nephew one of these days about encouraging his Dad. I sent my brother some information about free online courses in app development offered by a local college. His doctor thinks they got all the cancer out of him, but he will have to take some preventative chemo just in case. Maybe after that he can do something? I'm not sure. I just want him to be have some sense of personal accomplishment - he has told me he feels really bad seeing his former classmates have impressive careers while he has none. It hurts my heart. He is a gamer and is very self-educated about many topics including computing and politics. He enjoys cooking and does most of the cooking for his family.
I guess, in part, it depends on what you think his reasons are for not wanting to pursue an education... is because he feels like it is too late/he is too old/or that he just doesn't want to? Or do you think the main driving force behind not wishing to do this lies somewhere more within the fear; or more like a "block," of sorts. Similar to "writer's," maybe? But in the sense that, psychologically, he has never done it. Like everyone else (seemingly has). And now, it would just be really hard to (regardless of how easy he is told it would be) do so. For him, he just can't see it. Given how it's always been this sort of somewhat fear of the unknown. At this point, if it means something to him, it'd be, or have grown to be so massive or gross/as in 'large,' in scale or scope - that it is almost unfathomable, and therefore of the table.
So no amount of reason, therefore, is going to work on him or get him to change his mind. And that's assuming he wants to in the first place. You're right, in that, if you can get him to see that there is still time, and a future, then maybe you can begin to get him to see things another way. But if what I'm in part wondering is even partially true, then it's going to be ... a lot harder than it seems, or should seem. Because now at this point, and stage in his life - it has morphed or worked its way into this rather large, or big thing (deal) in his head & mind. Which we all know, is an incredibly powerful thing. If I think it, and I believe it, then it doesn't even matter whether or not it is true, or how true it is. Because it is true to me.
I'm glad to hear of his prognosis. Could be a seismic shift in his thinking; & maybe just take some time then, to adapt or adjust to this realization (that he's going to make it, and everything is going to be, "okay!"). Especially if he was set on it not being? . . . Maybe he is content with where he is in life. And that is that. If that is the case, is it o. k.? That it bothers you, should it (if it doesn't bother him)? I guess that's the tough question to ask, and maybe even more difficult to answer. If you'd thought that, changing his mind, or talking him into it were still a possibility - then maybe you could try to seek counsel from somebody in the know, who could tell/or inform you of the exact path, or route that would be reasonable & feasible at this stage to him. For instance, this degree will yield that job (likely). Provided that you think it is something he'd be interested in, again. Which seems to be the sticking point, or difficulty, at this moment~
Oh, forgot to say - because it seems so overly obvious to me, maybe? That you have a lot of very good reason to be happy for, and proud of, how he has turned out. For your brother seems to have lived quite a successful, fulfilling life. And doesn't appear, from the outside, to have let the bad things which have happened to him impeded his life (in an outward fashion). Maybe it's had an effect, and damaged him some on the inside, which you would probably see & be able to know. But to those not in the know, he appears exceptional. And to have thrived, in spite of~
I'm sure having a Sister like you, who was as good to him as you were (not that it's over of course by any means...) has helped immensely/tremendously/a lot! So you could, at the very least, take credit for that. . .