On the whole, most cover letters from applicants fall into the "average" and "generic" range. They reiterate something taken from the firm's website, talk about their leadership in X club, and say that they have always been interested in banking or consulting since an earlier internship.
This type of content is perfectly fine and shows your genuine interest in the field.
However, just listing a few main points to answer questions doesn't do enough to "sell you."
Where most cover letters fall short of being exceptional is framing their background in a way that is crisp, concise and compelling.
How to be CRISP
Firms are obsessed with their culture. But that doesn't mean you should talk about culture incessantly in the cover letter.
Make your points strongly and boldly, and then move on to another point. Don't refer back to culture more than once, or to one of your skills more than once. Recruiters have THOUSANDS of resumes and cover letters to read through, and if you make your writing longer or more complex than it needs to be, they may just skip over your documents and automatically reject you.
There's a term known as "MECE" in consulting speak -- meaning Mutually Exclusive, Collectively Exhaustive. Be as MECE as possible in your cover letter -- choose those activities and experiences that say everything you want to say while avoiding repetition.
When answering the question of "why work at Goldman/any bank?" nearly 90% of applicants mention a business principle that they are impressed with.
To make the cover letter even stronger, the most successful applicants demonstrate that they have met or even exceeded the business principle in the past -- through work at school or with an organization. Reviewers will be impressed with the applicant's understanding of the principle and how they've applied it in the past. This applicant will have higher chances of getting the job because the recruiter recognizes he or she will be a great cultural fit for the firm.