You're absolutely right and it's more about highlighting examples of your past experience and achievements that can be easily extrapolated with what they are looking for and how you can consequently add value if you were to join.
I would frame the cover letter more around "fit and potential" than "how you would add value". I know there's not a huge amount you can mention in a cover letter but overall, I would try to craft a coherent personal (this is super important!) story that covers the following three questions:
+ Why consulting: would be helpful to include max 1-2 lines around why you are interested in consulting (vs. banking, tech, etc.)
+ What are they looking for: most consultancies are very clear on what they look for in candidates. Without going into to details, which you can do in your CV, try to list/highlight a few examples of your relevant experience and achievements that link with that. (e.g., inherent passion for solving complex problems from your engineering degree, building clean water access in developing countries, engineering internship designing a new engine part, etc.)
+ Why a good cultural fit: this is an opportunity for you to show that you know more about the firm than what is on the website. You can mention (current and/or former) consultants who you have spoken with and things that resonated for you (e.g., diverse and inclusive teams, etc.)
(edited)