Ditto to everything Amphibian said above...
I would like to add that we have a growing number of retired airline pilots from AA, SWA, Spirit, etc. currently flying here (with many more applying), and the stepping stone is a two-way street. Many of us have done the non-regional 121 thing, and for various reasons, do not want to go back to 121.
Whatever your final career destination goals are, I wouldn’t hesitate to recommend flyExclusive to a fellow pilot. Decent pay, good, predictable 8/6 or 15/13 schedule, live where you want, no jeopardy company paid, full-fare airline ticket commuting to work, fly to and stay in nice places, and keep all the hotel, airline, and rental car points.
If the Majors are your goal, then a wholly-owned regional with flow to AA is your best bet for a stepping stone to the majors.