If you're talking to a "hiring manager" who "doesn't read cover letters", you've already conceded the game. Also, speak for yourself --- I read cover letters in advance, and often don't even bother with the resume until the candidate is in front of me.
I have no idea why you think most good candidates won't be "writing specific cover letters for your company". Top talent doesn't shotgun resumes across 100 companies; they pick places they think they'll like, have a reason for doing it, and do everything they can to get the best possible offer.
Why would you not read their resume before the interview?
I spend a good 30-45 minutes building a list of questions based entirely on the contents of their resume. I couldn't imagine just looking at a resume and then interviewing a person off the cuff. Seems a little rude.
It is rude, but this happens a lot, especially at smaller startups. The chain of communication is usually a bit chaotic and most people are very busy. Sometimes people get pulled into the interview at the last minute, and so on and so forth...
Why would you interview someone based on their resume? Why wouldn't you take 30-45 minutes across all your candidates to build a list of questions that were actually relevant to your business? The cart seems to be dragging the horse here.
I have no idea why you think most good candidates won't be "writing specific cover letters for your company". Top talent doesn't shotgun resumes across 100 companies; they pick places they think they'll like, have a reason for doing it, and do everything they can to get the best possible offer.