Isn't that the job of the cover letter to connect the dots and show how previous experiences & skills could meet the demands of the role being applied to?
Does anyone ever read a cover letter? In all my years of being an interviewer, HR has never once given me a cover letter along with the resume of the person I'm interviewing. I just assumed cover letters went straight to the trash because there's no way anyone in HR is going to have the time to read them all, let alone know enough about the role to glean anything useful from them.
I assure you, in the nonprofit space, cover letters are extremely important for contextualizing experience.
Sure, but even still – there's limited space on my resume. Imagine I've brainstormed 20 short "responsibilities and accomplishments" statements I can list for my last job. Of course I'm not going to list them all, but I am going to pick out the top four that make sense for the employer I'm applying to. I might put a different four on LinkedIn.