Even Super Mario Brothers, the pinnacle of games for years, had no save button and you have to pull off a long series of perfect play with only a couple of lives or get sent back to level 1.
Maybe the original has this issue of being held back by overly punishing arcade inspired design, but I replayed Super Mario World recently and I think it holds up in this respect. You only need to get past the next checkpoint for your progress to be saved, and if you are running low on lives and don’t want to lose progress, there is the option of going back to previous levels to farm more lives and powerups. There are also semi-secret areas with buttons that put extra blocks into every level that make the game easier. For basically the first half of the game the only thing that’s really required to win is a small amount of impulse control, planning and patience, and it seems to deliberately work to teach you that stuff in various ways.
Maybe the original has this issue of being held back by overly punishing arcade inspired design, but I replayed Super Mario World recently and I think it holds up in this respect. You only need to get past the next checkpoint for your progress to be saved, and if you are running low on lives and don’t want to lose progress, there is the option of going back to previous levels to farm more lives and powerups. There are also semi-secret areas with buttons that put extra blocks into every level that make the game easier. For basically the first half of the game the only thing that’s really required to win is a small amount of impulse control, planning and patience, and it seems to deliberately work to teach you that stuff in various ways.