Thank you and to everyone else who replied as well.Completely agree with @Nicole15! My only suggestion is that to keep the cover letter to a page and, since they have been specific about what they are looking for, ensure that you really flesh out your motivations for wanting to apply to Skadden and why you're a good fit.
A helpful way to do this is to relate your answers back to your motivations, traits, skills and aspirations for your career. For example, if you say that XYZ deal at the firm stood out to you, you should also say why this deal captured your interest and what you think deals like this mean for your training and career. Similarly, if you say the ABC characteristic makes you a good fit, you should mention how this matches with the firm's values/ethos and potentially how this characteristic will influence/impact your training.
Wishing you the best!
Their cover letter is limited to 300 words only, which is why I asked in the first place. Because they sort of set out what they are looking for in the wording of the question, and with such a limited word count, I wasn't sure if I should/can include much on "why law."
I would have followed the "why law" "why firm" "why me" structure in a longer cover letter.