It would be nice if you could see a response time and rate from a company on careers, much like you see an accepted answer rate. The biggest things that stops me from from writing a covering letter and applying is my past experiences (on other job boards) where I've written a letter and sent it into a black hole.
In addition to the solid point made by @TimeTravelingBobby, not all employers respond through the Careers interface. We email them your resume directly which probably includes some contact information for you. Many companies enter this into some sort of applicant tracking system that can handle all of their hiring needs (not just developers) and then they contact the candidates through there. Because of this, we couldn't possibly know the actual response rate.
Even if we could know the actual response rate, I would probably still be against this. The job requirements and responsibilities are much more important tools for deciding where to apply than their response rate. Even if some employer only responds to people that pass their resume scan, that percentage doesn't affect whether or not you will pass their screen, it's the content of your resume that matters. So apply to the jobs you are qualified for (or almost qualified for) and that you think would be interesting to you.
On the flip side, I understand first hand the feeling of wanting to know where you stand on an application. We cannot directly require employers to respond to applications through Careers, but I'd be open to any other ideas that address the issue.