Nitty gritty cover letter questions

As a sometimes-hiring manager myself and a connoisseur of idiotic chatGPT posts, I feel reluctant to write a cover letter that sounds like a cover letter. I.e., "My past experience at XYZ would be useful to Institution in this or that way," or something similarly structured. The description of the role I'm applying for seems to be eliciting someone with a lot of independent and creative thought, and I want to demonstrate that in my application. I also have observed that this particular type of museum is facing a lot of big, disruptive questions (as are many others, surely, but these questions are mega-specific to the genre), and I want to indicate that I am thinking about these things.

So I guess what I'm asking is, is it okay to describe my experience and projects through the lens of big ideas and questions as opposed to through the lens of how, explicitly, my experience relates to the day-to-day duties of the position? (It is a low-level curatorial role.) I think this would speak to the mission of the museum and the role no less. But maybe that's off-putting! I've only had one proper museum role so I feel inexperienced as an applicant.