Some schools do have rolling admissions. All schools have a limited number of interview slots. So many applicants apply early (my school could fill all its interview seats by taking one out of every two who apply on the first day!) By August, some of those interview seats have gone to the early birds. You are fighting the early birds plus the August crowd for the remaining seats.
If an adcom member is reading a good applications, the natural reaction is to recommend for interview - not to say, "let's see if someone better comes along a month from now". There is a little bit of holding for later consideration but for the most part we are snapping up the best with the hope of snagging them before they decide that 10 interviews is enough and that they can't afford one more trip (particularly if the interview date is late enough that the applicant is already holding an offer and can afford to decline an interview invitation). So with all this feeding frenzy for excellent early bird applicants, we often fill interview seats early in the process.
