Yes my thoughts too. Could be a great experience. I looked at a (POS) 172, pre COVID. 60K, I wouldn't let anyone I like fly in it, let alone my son or self. I would be very amicable to leasing a newer aircraft with an advanced cockpit, aka Garmin 1000, but I don't know whether 200-300 hours leases are doable for SE aircraft.

Well you are looking in the wrong place. You are not going to get your airliner grade equipment for that price. But good research and a solid pre buy you could get a descent rig for 40-60k. Put your time on it and sell it
Best of luck with your lease idea but even if you did the rate for a 800k cirrus or mooney ain't gonna be cheap.

That's the myth people like perpetuate but the truth is that lifer CFIs can make some of the worst instructors. They have long lost touch what it is like to be new to flying. At the mom and pop shop I used to teach at the "older" CFIs would find any excuse not to fly with their student and do ground instead. Why leave the comfy confines of the FBO for a cramped 152 you've spent 1000 hours in? They had many 75 to 100+ hour PPLs while my students were getting theirs 45 - 55 hours.

I agree you're likely to get a cheaper price here. You could get better training but I'd like to point out that the lack of organization and structure that is typical of the described scenario can be a problem for some.

I also taught both 141 (at first) and then 61 (later). My part 61 was also very structured with documented curriculum and constant follow ups to keep students on track. I didn't meet another part 61 instructor that was that structured though. But that was 20 years ago. Maybe things have changed. When someone says part 61 instruction at a mom and pop FBO I tend to think of some old geezer as CFI hanging out on the weekends mainly to do rental checkouts but has an occasional private student who when he shows up "hey, let's go fly".

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lol und oh no way! My favorite pilots to run into. It’s like talking with a vegan Crossfiter, they shout it as soon as they walk in the room. Don’t get a useless aviation degree. Get something that your kid can use when the industry is down or gone, ya know flying cars and all. Separate from the degree go and do the flying stuff. If your kid can do some active duty in the military he can get Uncle Sam to pay for a fantastic flight training program at a community college. If you do it right they pay for the tuition, flight fees, and give him a housing stipend as well.
if he doesn’t want to play soldier, do what was stated earlier, buy a mid range Cessna and fly around the country with your kid teaching him how to be a good aviator. Those are experiences and memories you would both cherish for the rest of your life.

If I did it all over again, I'd enlist in the air force in an IT field. Learn everything I can for at least 36 months, then get out and use post 9/11 GI bill at a university with a flight program. Get my licenses and IT certs at the same time. Maybe even join a ANG unit and put in for a UPT slot every chance I got.

Hindsight 20/20.

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This is what I’ve done, except I was in the service for 9 years during the lost decade. I say have your son join the military, either go the commissioning route to fly or just 36 months of service in a field where he can gain some backup skill sets and get the GI BILL.

After that, recommend him to to use the GI BILL to get the remainder of his ratings and check the degree box. Plus side to that, by the time he is finished with all that, the industry hopefully will have shaken out.