The exchange of money does create a business transaction and not giving an answer to the applicant is UNPROFESSIONAL (and unprofessional is a really civil way to put it).
As I see it, it does not matter to the applicant how their fee is ultimately utilized by the institution. The fee is payed for a yes/no answer, and the argument that the department doesn't receive the fee directly, and therefor not bound to respond in a timely and professional manner, "has nothing to do with the price of the rice".
I also agree that this is a giant red flag when selecting a program to enter, however I am alarmed by the frequency of this behavior by graduate programs (in my case 3 of 6 PhD programs sent no answer). I have now received notification from 2 of those 3 programs but only after contacting multiple people, multiple times, over a period of 2 weeks. If this is S.O.P. than revision is required.