This may also depend on airport? Last time one of these occurred for my friend flying from ACT (Waco) on the early morning flight, she was surprised to receive a notification the night before. That airport is tiny and getting there early is not fun for no reason. She called AA and found out crew rest was the reason. The plane coming in to DFW was late and the crew would not be able to fly to Waco without the mandated rest hours until at least the stated delay time. That was without question, but again, ACT is a small airport. Had it been DFW or ORD, the chances of changing a plane or crew could come into play. In my friend's case, the 5:30 a.m. flight was rescheduled to something like 8 a.m. Waco is a very nice little airport, but arriving at 4:30 for the only flight and airline would have been futile that day.

To update... the flight did indeed get delayed. In fact the amended departure was 9:30 but that was moved to 10:00 as they were waiting for the 1st Officeer to arrive from DFW. Finally got off the ground. At least the 3 hour layover in PHX will come in handy.
Thank you everyone for pitching in with information and insight.