The analysis for why such exposition wasn't necessary in SMB:
http://www.auntiepixelante.com/?p=465
I think part of the problem with modern games might be the increased freedom. SMB had much less freedom than a modern 3D game. When the player has less freedom, it's easier to construct levels that push the player into a certain direction. Certainly, a first-time SMB player can avoid what Miyamoto set up, but it's not likely. The more freedom a player has, the more variables there are to contend with in level design, and the harder it is to nudge a player towards certain discoveries.