What do I need to include in a tenure-track assistant professor job application cover letter?
I'll be honest about when I read packages (in chemistry). The first thing I look at is the CV. I also skim the cover letter. Then I read the recommendation letters and the research and teaching statements. Depending on the CV and recommendation letters, I may take more or less time on the research/teaching statements - if the candidate seems promising, I'm more thorough.

But if the cover letter is short, not tailored at least some to our department, contains obvious typos, etc. I'll get a bad impression.

Look, anyone applying to a tenure-track position has taken a lot of time to get to this point. You've secured a PhD, possibly gone through a postdoc position, and prepared the whole application.

Why spoil it with a lousy cover letter. Take some time, think up a paragraph or two about a particular department, consider what you might add, and let us know.

This tells me that the candidate is not just blindly sending out a gazillion applications.

I doubt everyone completely rewrites their cover letters for each application (I didn't). But I do want to see that someone has taken the time to carefully craft a paragraph or three about us and how they might fit.

Will we interview someone who seems stellar with a poor cover letter? Probably. But we also get ~100 applications for every opening, so why would you risk it?