It sounds like BPF's example is one end of the scale, which can certainly exist, but is also generally detectable. The buyer could have had an effective inspection done on the plane, and found much of this before choosing to purchase. That need not made the concept of buying your trainer sound like a bad idea, just do your due diligence!
......and even after getting that expert advice there is still a possibility that the 45 year old Cessna 150 you are thinking of buying could give you huge unexpected maintenance bills at any time
is true. But, I defy anyone to be able to spend so much money
repairing an old 150/152/172 to the point that it costs what a new 172 costs! Yes, you can make a big bill modifying it up, but keeping an old basic trainer airworthy can be done for less than cost of a new one.
If the owner gave it to you, you would still spend more getting it airworthy then it would be worth.
I know this was tongue in cheek, but there is something to it. I have seen whole aircraft sold for near scarp prices. Some damaged or disassembled. The right person making the right investment gets a good plane out of it. But, that investment will not be returned to the purchaser after only a couple of hundred hours flying. Think long term, maybe you want to keep the plane for a "long time", and fly the value out of it for yourself.
Renting to train to the PPL level has very predictable costs. Post PPL, whatcha going to do? Keep renting at that same cost? Renting a training aircraft, with limited choice as to where and when you take it? If you're happy with this, rent. Ownership offers more freedom, and the associated risks, you don't get anything for nothing. There is a minimum cost to fly, as the people upon whom you must depend to keep the plane flying expect to earn a fair living like anyone else.
Canada has burdened itself with a silly complicated and expensive airworthiness system, which extends much too far beyond simply good wrenching and lubrication of aircraft - way too much paperwork of very little added value. But, that's the price we have to pay to fly freely. So many counties simply do not enable GA at all, or at a bearable cost. If you can afford to smoke, drink and watch cable TV in Canada, you can afford to fly modestly, and probably own - as long as you surround yourself with wise people to help you avoid the pitfalls which are out there.
and a radio [Radair] that nobody has ever heard of
Yup, that's me again, the nobody!

I've flown with Radair radios, and no, they are not worth fixing. But then most radios from the '60's and 70's are no longer worth fixing either. Some things just get obsolete. Would you fix the 8 track in the used car you bought? A purchaser of used aircraft has to realize that some avionics are just not worth any repair investment - replace.