I guess maybe we need to agree on what kind of "reliability" we're talking about.
If there are indeed more recalls now than there were 40 years ago (and I'll take your word that there are), is it possible that the reason is simply because there are more car manufacturers now than there were 40 years ago? That they're selling far more cars, and thus, when a problem is found with a particular model, there are 150,000 to recall instead of 30,000 in 1976?
Finally, I'd also question the nature of the recalls. Are they for safety issues, or because of a faulty toggle switch on the motorized seat adjustment? Is it for a brittle crankshaft, or stitching that frays too easily in the leather upholstery?
As far as "reliability" goes, if we're talking about "do I trust that this car is going to start and get me to my destination without stalling," I would say that modern cars are far, far more reliable than cars built 40 years ago. To deny that would be to claim that the industry has learned nothing about improving reliability in the intervening 4 decades, even in the face of increasing competition.
This is true to a degree, although I question what percentage of owners did much of their own servicing 40 years ago. Was it appreciably higher than the percentage today who would do the same servicing, were they not blocked by increasing computerization?
Finally, with the increase of economics of scale, miniaturization, and cheap outsourced manufacturing, nowadays it's simply much cheaper and faster to replace a broken component than try to repair it. I'm not dissuaded by the fact that I can't get into my radio and re-solder the transistors - I can simply go on Craigslist and find a replacement unit for $50, and swap the whole thing out. Oil changes and light bulb replacements are still easily done by owners. Do I care that it's gotten harder for me to replace my own O2 sensor? Of course not - cars 40 years ago didn't have O2 sensors. They just sprayed exponentially more toxins directly into the air. I can't tune my carburetor either - modern cars don't have them. It's fuel injection, controlled by a microprocessor (instead of a distributor cap). These are all improvements. Increased complexity, for sure, but they've brought with them a commensurate improvement in reliability.