Unlike pop artists, we piano improvisers aren't limited by the confines of a 3-4 minute recording, which is the length most hits need to be. (Some big hits like the Beatles "Hey Jude" are longer, but they're the exception, not the rule.)
This gives us a lot of artistic freedom that even the original artists didn't have. It's actually more akin to how jazz musician take popular songs from the 1920s - 50s and "do their own thing" with them, stretching and expanding the material as they shape it according to their own personal tastes and preferences.
You can play pop and rock songs like this too.
Do you like to play rhythmically? Great! Take a gentle pop ballad and bring some of your unique rhythmic energy to it. Do you enjoy playing improvised solos? Wonderful! Solo over the chord changes to a song of your choice.
I've made a video to show you what I mean by this. It's the Beatles song "You Never Give Me Your Money, which is part of the famous "Abbey Road medley." Even though the Beatles just quickly go from section to section, each part has the potential to be treated as a song in itself. On the video, you'll hear me explain a little bit about how I expand each section with improv, and then I jam on the whole song.
Enjoy, and then try this with a song of your choice!
You Never Give Me Your Money: Complete Beatles Piano #12