I have worked in financial aid at several schools, all FAFSA-only. The EFC was used in two ways: One, to award federal aid within the regulatory guidelines (Pell as required; SEOG using an institutionally developed formula to award the pot of federal money to students with the lowest EFCs; FWS using institutionally developed formula to award the federal/institutional pot of money to a subset of students based on EFC and factors involving packaging parameters; determining subsidized loan eligibility). Two, to allocate the limited institutional funding among the student population in a manner determined to best assist the neediest students. For example, at one school we awarded students with an EFC under a particular number a package of grant aid (Pell, SEOG, institutional) that equaled tuition for 12 credits less their EFC.
We did not promise to meet need at any school where I worked. Thus, EFC was simply a number used to award Pell and to allocate the limited pool of federal/institutional grants & FWS. Oh, and it came into play when determining whether/how much of the student’s federal loans would be subsidized.
At every Federal Student Aid conference I attended, aid professionals requested that the Department of Education find another name for EFC.