When hiring staff members that need to be able to write documents as part of the job and explain things clearly, the cover letter can make a significant difference. Most good candidates do write ones specific to your company. A generic cover letter is an extension of the resume (at best) and often an indicator of a lack of interest (at worst).
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.
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.
If they are generic form letters that have been obviously sent to everyone without any modification, then I probably won't even talk to the person applying.
If they aren't interested in what we're hiring for, it makes me a lot less interested than what they have to offer.
But, my experience on the other side of the table is that I've never actually gotten a cover letter passed on from HR. Or, if HR gave them to the hiring managers, they didn't pass them on to the engineers reviewing resumes & doing interviews.
Maybe there's a strategy here:
Cover letter: I love frat-houses and beer! I want to bring my spiky hair to work for you!
Resume: When I'm not submitting patches to the RoR team I'm writing Scala code for my EC2 cluster.
It's a shame the economy is so bad. It would be fun to do some exploratory job hunting to see if this strategy would work.