I suppose they might, but I've been around long enough to have owned and driven a 1950 Studebaker and I can say for sure that new cars are much more reliable abd trouble free than cars were back in the day.
Also, a 2007 Toyota Camry would be a lot easier to push than a 1979 Chrysler!
But to answer the original question, No, I've never had my car stall in traffic while dressed. I once heard the "thump, thump" of a flat tire, but when I pulled over and looked. I had run over part of a plastic hub cap and it was stuck in the tread of the tire. I pulled it out and all was well.