Let me just drop this in here. If this thread ever gets zombied awake I’ll feel confident people will remember the 2020 plague.
THIS. EXACTLY THIS.
An "iconic" theme would be the ones from Marios, Zeldas, and Animal Crossings.
Why you ask?
Because the "theme" is carried around throughout the entire soundtrack of said games, and across different iterations of them, in different variations. The latest clear example of a "proper" theme would be the Mario Kart 8 Deluxe theme. The same theme is being carried from SNES all the way to the Switch, in different ways, and different arrangements, all while maintaining a clear reference to its origins and what's it about.
Heck, I often play Mario Kart Tour and even there you can clearly hear the different Mario Kart themes.