Is it common for institutions to require 3 completed letters BEFORE an interview?

I've been invited to the next stage of the application process after applications have been reviewed. This is for a postdoctoral fellowship in humanities (Classics). They requested that I send in three recommendation letters with a two-week turnaround. I expected them to be fine with a list, at least before decisions are made. I have one letter completed, two requested. They've emailed again that I need to have those letters completed or I won't be considered. I've told them that I've reached out to those advisors. I haven't had a request for an interview yet. I'm wondering is this common? It's a bit frustrating and I'm wondering why reject potential candidates for the negligence of their advisors? Especially when they haven't even interviewed yet.