Southwest will proably be a bigger and denser version of its present form in 15 years. They'll probably add Canada, Mexico and Caribbean destinations if they can be added without a substantially higher per-pax operating costs than US airports.
Don't look for WN to enter LGA or JFK. They'll probably keep up the 'bracketing' strategy, say Newburgh for New York, Trenton for Philly, and if they go to CA Hamilton for Toronto. Also possibly Rochester MN for Twin Cities as to avoid a direct brawl with NW. (Driving dist 76 miles, a bit far but feasible).
In 15 years, most Americans will probably live within a 120-150 minute drive of a Southwest city. EG Columbia for South Carolina, Richmond for Virginia, Des Moines for Iowa, Milwaukee for east Wisconsin. They will blanket medium-size and less-congested large destinations. And maybe get to Rochester NY and stop making us drive to Buffalo (sorry, I have to mention that).
Which brings up another question I haven't seen discussed at airliners.net: will there be low-fare regional service in the US? ATA now operates "Chicago Express" regional service to SBN and other regional airports with SF3's, and Shuttle America is a free-flying regional with Dash 8s in the Northeast. But no one has created large scale regional low-fare flying yet. I don't know why, perhaps no one has figured out an economic formula for it yet.
If anyone can do it, Southwest can. Say pick one a/c type: CRJS or ERJs, probably ERJ's cause they have a 37 seat model and offer low-end flexibility. Then Southwest could bring its low fares to places like Billings MT, Fargo ND, Charleston WV and Rapid City SD that are far more than a 2-hour drive from any medium-size market WN could serve with 737's. And they could feed WN hubs at IAH, STL, BWI, MDW.
And again all this depends upon whether WN and other large low-fare carriers survive superconsolidation of the mainline carriers. If the supermergers are allowed, Big Air would have the critical mass in individual companies, to try to destroy the icky margin-eating presence of large low-fare carriers.
Need a new airline paint scheme? Better call Saul! (Bass that is)