I’ve read elsewhere that I need to tell my “story” in a cover letter. Why are you saying that they should be short?

First, few people (in investment banking) read cover letters.  You are going to get judged almost exclusively on your resume.  And generally, the only time a cover letter will have an impact on your chances is if you say something stupid or have typos.  That is to say, cover letters (or cover emails) are usually necessary but are likely to hurt you more than help you.  So since (1) few people read them and (2) they are more likely to hurt you, you might as well keep them short and to the point.