It's an hard-to-debate fact that Super Mario Bros. 3 lit the gaming universe on fire with enjoyment when it was released back in 1988. Still the definitive Mario game for most people, it went far beyond emulation for John Romero and his team at the soon-to-be id Software. They made a demo two years later in 1990 that they were ready to pitch to Nintendo.
John Romero shared a link to a video of the demo via his Twitter in celebration of the 25th birthday of iconic computer game series, Commander Keen, which was also developed by id Software. The demo uses elements of gameplay that would go on to form cornerstone mechanics of id Software's beloved platforming series.
Super Mario Bros. 3 Demo (1990) from john romero on Vimeo.
It's hard to say what Nintendo actually though of the id-developed SMB 3 demo, but its easy to speculate. Nintendo was a powerful force and nearly a monopoly in the video game industry back in those years. The company had a stranglehold on development of video games, especially when it came to Nintendo IPs, so it's easy to guess that they probably wouldn't have ever let the id software ever hit the shelves on any platform that didn't have Nintendo's brand plastered across it.
Nonetheless, take in the interesting creative design of id Software and John Romero's port of the game and then go look up some Commander Keen while you're at it. Those folks had the right idea.