Schools are judged, in part, by competitiveness which is measured by the proportion of applicants admitted meaning that they want the maximum number of applications possible so that the proportion admitted is very low. They also want to maximize yield which leads some to only admit those applicants they expect to matriculate (thus the desire on the part of some schools to get applicsants to express their continued interest after interview).
Schools know that there are some applicants who are turned down for early decision and who will therefore have their applications to other schools arriving in the late fall. Remember, schools want applicants even if they won't be able to admit them.
Schools start interviewing in August or September. Every interview handed out is one less interview slot you are eligible for when you apply after interviews have started. Schools might be more generous in giving interview invites early in the cycle until the quality of the entire pool is determined and schools become less likely to settle for a less than stellar candidate. On the other hand, if the pool is weak, it might not matter when you apply, if you are easily in the top 10% of appilcants to tht school, they will find an interview slot for you.
Also, human nature being what it is, it is easy to be jaded late in the season and have it take more to impress an application reader late in the season than it was on day one.
