You were definitely supposed to start from the beginning each time you played, and you'd get a little further each time you played. You'd know the earlier levels by the back of your hand.
Your final run might be just an hour or two, but it was the product of many more hours of practice.
I don't think games ever expected people to keep their consoles on overnight. Games of that length had saves or passwords.
Even for games that had unlimited continues, you were often expected to select "No" on the continue screen eventually. You'd restart with your new knowledge and get to the same point with more power ups, more lives, etc...and you'd use your newly-gained knowledge and skills to get more of those resources in the earlier level, making the later levels easier.