What a regional would need to succeed as a stand alone carrier:
Efficient Aircraft-
Short segments have to be flown on turboprops, unless demand dictates a large RJ. You would need jets at CR9/E175 size or greater. 70 seats, 50 seat, 35 seats on a jet just won't pay the bills. Not to mention, these smaller RJ's have enough limitations to make for a level of customer service that a new airline could not tolerate. As for props, the bigger the better. I think an ideal regional stand alone fleet would be made of Dash 8 300's and E 175/190 aircraft. Both types are roomy for their "genre", and very capable.
Point to Point route structure-
Skip the hubs and fly people where they want to go. You don't need every passenger, but pick who you want and make them happy. If your product is good enough, people will drive to your point of departure. Also, hubs lead to so many missed bags, missed connections, and "delays beyond our control". These are all detrimental to developing a customer base.
Large market internet sales and advertising-
You need to start out on expedia, et al. if no one can find you, you won't sell tickets.
Appropriate fleet size-
You can't start out with 80 airplanes on day one. Add planes as you add service. Independence started out way too big. You need to to fill all those seats...
The biggest downside to starting up is that no one knows who you are. People won't save $5 a ticket by booking on an unknown airline, unless you are giving them exactly what they want.
By reading the above criteria (props, jets over 86 seats, point to point route structure, focused market share), you end up seeing the model of most US domestic airlines in the 70's and 80's. This worked. Everything went to pot when the jets got smaller and the props went away. The RJ was a noble appeal to the customer, saying here is a jet to replace those noisy props you don't like. But, the RJ wiped out BOTH smaller mainline aircraft AND newer, more efficient Prop regional aircraft. Imagine fleets of Q400's and Saab 2000's and ATR 72's kicking it through the northeast and deep south, flying faster at the lower altitudes, out of the way of the faster jets. Thanks Delta.