MBB firms (McKinsey, BCG, Bain) usually require a cover letter. They'll read it immediately after reading your CV, provided your CV has captured the recruiter's attention.
Do you need a cover letter for McKinsey?
Cover letter is not required.
Do consultants need cover letters?
Consulting firms will typically read your cover letter to quickly identify what makes you different from thousands of other applicants. Therefore, writing a strong and unique cover letter can make you stand out from the competition and ensure that your achievements aren't overlooked.