Could you give an example of such an intro? I'm not entirely sure what style you are referring to and am quite curious.
Duh.. Duh.. Dih dih dir! Dir Di dih dih dir dir du du duh! - Star Trek - Next Gen
It does not have to be original. And I don't mean only the intro but the entire soundtrack. Often, the theme song is reused over and over during the film with many variations to set the tone of a scene.
Bad movies skimp on soundtracks.