Actually in a recent artical (Mishpacha Kulmas) it said that the rules of LO ADO ROSH is to prevent Yom Kippur from falling on Friday and Sunday so that there wouldn’t be two days of (total) issur malacha in a row, and also that HaShana Rabba should not fall on Shabbos.
Yes, I knew that the calendar is also jury-rigged to prevent a Yom Kippur Sunday and a Hoshanna Rabba Shabbos. I specifically only mentioned Yom Kippur and Friday because the thread is about fast days on Friday.
The Wolf