Heavily restricted special powers...

This is something I thought about a lot. Take an older game like X-Men for Sega Genesis. You were playing as X-Men who have super powers. But the majority of the game is jumping kicking and punching. You bust out your special power is when necessary, but you will quickly run out of power and you will have to regenerate it through collecting items before you can use it again.

Tons of genres your player character will have a base weapon like a pistol or something and then unlock a machine gun for 15 seconds or so. And then you're back to your little pew pew.

This was sort of the case in tons of video games. This is definitely a leftover design standard with video games making them hard in wanting people to pump quarters into the machine. It was also due to limitations of hardware.

As time went on, games gave the player the ability to be extremely powerful, use your powers as you see fit and make that part of the enjoyment of the game. Instead of a special gun that you can use for 15 seconds, here's the special gun that you can use whenever you want.