It's a simple long tail problem. People tend to be grumpy if they don't get a response (at least some people will be, statistically speaking). Those people will likely act as negative multipliers when it comes to your organization (especially since some of them will already be in a bad mood if they are job hunting out of necessity). They may or may not be less grumpy if they get a response, my hypothesis is that at least some of them will be less grumpy. If you get 200 replies for each job posting and presumably post a couple of jobs, preventing some negative feedback (especially in the age of social media) for a modest amount of work should be a no-brainer.

You can chose to have a "clearly spam" category that you don't reply to I suppose but apart from these even the worst written applications deserve the decency of an answer (personal opinion). Similarly I also think even the most brain dead customer requests and support questions should be answered (once again personal opinion).

The benefit is obviously very hard to measure which is why I can only make an argument based on reasoning (or dogma I suppose). The cost however is really easy to measure so the counterargument is easier to make.