Its common for thousands of applicants to respond to a posting, many of whom are not vaguely qualified. So when a position is filled, its not uncommon to be turning down several thousand people.
Honestly, do you want to send a disappointing email to 3000 people and then deal with the responses? More importantly, do you have time? Remember, wasting time on the wrong problems is a sure-fire way to kill your business.
That said, if you've responded to a candidate at all, much less had an interview of any kind - then absolutely, you must follow-up. Those people have good reason to believe you might be an opportunity for them, and you owe it to them to respond one way or the other ASAP.
Sidebar: the current situation is awful for employers. Some start-up, PLEASE fix this. A job board where candidates can only submit 1 application per day would be a tremendous step in the right direction.
This in marketing departments for high tech firms, mind you.
Clearly, they a) don't care, and b) know they can get away with it.
When company has a job opening - they want to fill it ASAP, so they want to see multiple resumes, not few.
Even if these resumes are not 100% relevant.
In order to deal with high volume, recruiters choose not to reply to not very relevant applications.
In order to fix it, job board must be able to filter irrelevant applications, but realistically only recruiter [somewhat] knows if application is relevant or not.