Old cars being unreliable comes down to two factors.
a) They need continual maintenance, which is often underestimated, neglected, or done wrong. Most often people push parts beyond their intended service life.
b) Almost no old car has been properly maintained. So even if you manage to do everything to maintain your new old car, it'll have been compromised by lackluster maintenance, at some point in its life.
So, if you shell out the big bucks to completely restore that Trans Am back to factory new, you'll have a completely reliable car - if you observe the maintenance schedule rigorously. I, for example, have to grease the front control arms bushings, and steering ball joints, every four months. Not very many of people manage to service their car every four months...
I can add that I had a 2000 (with 200k on the odometer) Opel Zafira that burned oil, just fixed a burned valve on my 2011 Skoda Fabia because it burned oil (177k), and have driven (110k) in my ridiculous Cutlass with its poor 70s technology, without a mechanical engine failure.

The big lazy carbureted, NA V8 just keeps going. I've had fatigued frame bolts snap, though, and a poorly made aftermarket lower control arm, electrics and body rust - but the heart won't quit.