Scheduling won't ruin an airlines reputation. Crashing the planes is what ruins an airline. Southwest has only ever had two passenger deaths and one of those was an attempted hijacker beaten to death by other passengers.
Eh, to a first approximation the FAA won't let you crash the planes. It's been 13 years since there was a fatal plane crash on a US passenger airline.
FAA has an important role, but market forces won't tolerate an airline that experiences crashes, even rare ones. Airlines are highly incented to be safe, both by regulation and by the market itself.