It's like the response to my PhD application usually includes something like "The number of the applications we've received is so high that we can't accommodate all of the qualified applicants." It's like outnumbering applicants is the general reason of rejection.
Besides that, they seldom address other reasons. Some responses of this kind were due to my enquiry after application, rather than on their own initiative. Some of them didn't bother to respond even after my enquiry.
So I wonder whether a research group or school actually reviews every applicant's documents if they receive an overwhelming number of applications compared to the vacancy number. Maybe they have a way to pick some among the large number of applications — like using the filter function of a computer to pick documents containing some kind of keywords, which may not be completely faithful — to actually review to consider who to admit and that's why they don't bother to reply to all the applicants they don't admit.
For example, recently I found the reason I was not admitted for an application to a fundamental physics research group in Europe four months ago is eventually the funding is only available for a research project which is not my research interest; thus probably they even didn't review my application as they, saying they received an extraordinary number of applications, only picked those whose research interests involve that research project to review.