Or is it just legacies and athletes that get in EA? Is there any competitive advantage at all to applying early?
There may be a very slight advantage to applying SCEA, however I believe most of the bump in the admission rate can be attributed to recruited athletes, legacies, and children of faculty, staff and dignitaries.
^Also the applicant pool tends to be significantly stronger in the early pool. SCEA applicants generally have their acts together with high scores and stats already in the bag. The SCEA school they choose is probably one of their top choices so it is likely their school specific essays are more compelling, especially the “why X” type essays. Less competitive applicants trying to “win the lottery” tend to submit in the RD round. H and Y specifically state on their admissions website that the higher admission rate in the SCEA round is attributable to a superior pool and not because there is an advantage. There is some argument that because there are less applications for the AO to grind through in the early round and that all seats are open so that those in line first have an advantage, EA applicants have an advantage. If there is an advantage because of those two factors, IMO it is at best slight.