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.