The problem is more one of cost and efficiency. You can still run your care for 100k of miles (the 1M miles is fiction, imho). But when e.g. the engine is broken, you don't fix it anymore but replace it wholesale. Less hassle, guaranty on the new part by the manufacture and generally cheaper: The old engine gets sent to the manufacturer for refurbishment by people only doing this (and hence more efficient than your run-of-the-mill mechanic).
Furthermore you can't fix a car do-it-yourself-style anymore because these things have become way more complex. So running a car _way_ past it's economically sensible lifetime (if you'd factor in the labour cost) is simply no longer possible.
And even old cars totally overengineered do fail all the time (my brother has a bunch of them). But since it's usually just for leisure, labour cost doesn't count. And because the parts are simpler it can usually be fixed.
So I'd blame this on the massively increased labour cost/car cost ratio. Go to a country with really cheap labour and it all works like it did here half a century ago.