I only fly SW to Vegas, they are they only nonstop carrier from SAT. On longer flights I fly a carrier with assigned seats, even if it means a layover or plane change. Usually they are $20 to $30 more than SWA,
My most recent experience with SW was in November flying out the Monday before Thanksgiving and home on Thanksgiving Day. Mom & I took the earliest flight to Vegas, it originates in Houston and stops in SAT then Nonstop to Vegas. Usually this flight is easy to find seats, since folks in Houston would have to get up really early to get to the airport. We were advised to be at the airport 2 hours early for security. We were through security in 20 minutes, and then they started lining up for boarding passes 1 1/2 hours prior to flight. Fortunately we near the front of the line. By the time the agent actually began handing out passes, the line was very long. OF course, as soon as most people get their boarding pass, the begin to line up at the gate. It was a full flight going out. Since we were only staying 3 nights we made do with 1 small carry on each, no checked bags!! The baggage handling in Vegas, no matter what airline, is S-L-O-W.
The airport was pretty empty on Thanksgiving for our return flight. We walked right through security. Again, though, folks started lining up 1 1/2 hour prior to boarding for their passes.
I'd probably fly SW more often with assigned seats. It's not like it is a hard thing to do.