I can understand why some people enjoyed SMB3, Super Mario World or consider that Mario64 came as a model for future 3D platforming, although I never really enjoyed them.
SMB1 I could never understand why people like it: Weird inertia and bad collision detection (maybe it was good when the NES came out but I never touched a NES before the 90s).
To quote one SMB3 review from GameFAQs (also mentionning SMB1)
Worst of all easily relegates the game to a 9 -- the collision detection. ''Collision detection'', in case you didn't know, means how you make contact with enemies and items. ''Super Mario Bros.'' had terrible collision detection, but ''SMB3'', five years later, makes little or no improvement, and it can be a problem. If you don't jump exactly on the enemy, you could get hurt. Watch out for them Micro-Goombas -- it's easy to get killed instead of making a successful jump. Various contact problems occur every now and then throughout the game.
As for it being a "pure" platformer sorry but no:
2) water/swimming levels