From what I recall of the debate surrounding deregulation, the main benefits cited by proponents of the then-pending legislation were to allow the airlines freedom to give the travelling public what they wanted and fares that more people could afford -- which were largely one in the same.
Once deregulated, the airline marketplace promptly sent the message that what the public wanted above all, beyond the basics of safety, reliability and respectful treatment, was more reasonable fares for air travel. Frills were of far lesser imortance, and of minimal or no concern on short-haul flights.
Since Southwest is consistently ranked #1 in Customer satisfaction surveys, they have obviously been successful in giving the public what it wants. From its beginnings before the dawn of deregulation, Southwest's record in the areas of safety, reliability, and satisfied Customers is unsurpassed by any U.S. airline.
Southwest has also been, by far, the most significant factor in keeping air travel within the means of more people. If anyone thinks the other major U.S. airlines share the same agenda, take a look at fares in virtually any market where Southwest or another no-nonsense, low-cost carrier is not present or nearby to spoil the price-gouging parties of the full-service majors.
Therefore, how anyone can suggest that Southwest in any way killed deregulation is far beyond my comprehension. If anything, Southwest has kept the true intent of deregulation alive by making it an unavoidable issue (how else does one explain United Shuttle, Delta Express and MetroJet?) by its eminent success in giving the public what it wants most: safe, reliable, air transport at reasonable cost.
Moreover, the unrivaled financial success Southwest has derived from giving the public the basics it most wants in air travel has no doubt inspired others, including jetBlue, Air Tran, ATA, and Sun Country, as well as Westjet, easyJet and Ryanair, to give the public more opportunities to chose what it wants most when travelling by air.
To answer the two-part question posed by the starter thread of this topic: 1) "A thousand times FALSE!" to the notion that Southwest may have killed deregulation, and, 2) "A thousand times TRUE!" to the observation that Southwest has proven that a no-frills airline offering low-fares could survive -- and thrive, through good times and bad -- by giving the public what they most want when travelling by air.