The problem is the defination of a platformer game. I don't consider Flashback as an platformer, it's more like an Action Adventure. There are also too many subgenres, platformer single screen, multi-screen, scrolling screen.
The last category is probably the most popular, with games like Super Mario, Giana Sisters, Super Frog, Rayman etc. Some games use "up", some a second button. I can live with both, if the controls are accurate enough.
Yes, this is only a fast scrolling platformer. You cannot enjoy the gameplay. I wonder why it became so popular.