The any% run basically hinges on skipping the unlock of Cher's Believe.

In normal gameplay, you would unlock this song after a certain number of points. By doing poorly enough on every song to just barely pass, you will avoid unlocking the song. If the song becomes unlocked, it is then required to clear it in order to finish the game.

It's not necessary so get the "secret" endings (fail all in-song gag scenes but still pass in the end), but it helps keep you on track for skipping the unlock.

This is also why any% runs should be done from Clear Save Data as this will re-lock the bonus songs.