Super Mario Bros 3 game manual [pdf]
gamesdatabase.org
gamesdatabase.org
There was also the way it was revealed, with the placement in "The Wizard". Hard to explain the degree of hype around that movie for elder Millenials of a certain age. The PowerGlove reveal, for one, but then the sneak peak at SMB3 at the end.
It's really cool that 3 worked on the same hardware more or less as the first Super Mario Bros. (Caveat that cartridges themselves could pack a whole bunch of technological tricks up their sleeve.)
Playing on an original system, the controls are so responsive, the scrolling is super smooth, and the game manages to mitigate sprite-flickering much better than other NES titles.
It's definitely crazy when you compare it to the Famicom/NES releases of the mid 1980s.
But as you said, cartridge-based games can be used to augment the existing hardware in a system. I think later SNES games included extra hardware in the cartridges to do accelerated graphics in games like Star Fox and Doom.