Piano introductions give us pianists a big opportunity that goes way beyond their minimum function of setting the key and tempo:
They let us state our point of view.
This is a big deal, although it's often overlooked.
It means that we pianists can establish a point of view about the song even before the melody comes in. Do we want to make it playful? Or flamboyant? Or tender? Or mysterious?
Don't waste these opportunities. The next time you're asked to come up with a piano intro, establish a definite point of view.
The Beatles did this, and so do all the other musical greats. Elton John does it too. Here's one of his greatest piano intros: