Great read, especially liked the call-out of the Smash Bros aMSa video: https://www.youtube.com/watch?v=2WMBwFO65J4&t=11s and Baba is You.

Correction: In Super Mario Bros., the 2D successors, and Super Mario 3D Land/World, Mario does indeed become Super Mario when he picks up a Super Mushroom. "Super Mario" is the name of his larger form.