Any old school gamer dealt with this ALL THE TIME.
Make it through all 8 worlds and get game over? Guess who's doing it again? Made it all the way through the final dungeon only to be killed by Ganon? Guess who's gotta bust their balls to get through the dungeon again?
The accomplishment garnered by beating something used to come from the fact that it was beaten when the player played near perfectly, or perfect enough where he was able to make it through all the trials without encountering a death/game over, causing him to have to start all over again. That was skill. That was something worth showing.
Nowadays, gamers get the same feeling by going through a level with a checkpoint provided every few minutes of gameplay, with infinite lives. It doesn't compare, at all. Especially when you consider the fact that older games tend to be harder than newer ones.
This is also the reason I can be proud to say that I can speedrun the balls off of SMB, or SMB2J, or hell, even SMB2 USA. Few modern games even give me the same satisfaction for being able to BEAT them. Ninja Gaiden is one of the few that did, and yes, it does have infinite lives and checkpoints, but man are those some scattered checkpoints...