Using the most recent data available (NOV 2014)
Southwest, with its herd-of-wild-elephants boarding style is only on-time 80.28% of the time. They are late to the gate 9.36% of the time.
One of the legacy carriers you refer to (whom I have been using) is Delta Airlines at 86.82% on-time. They are late to arrive at the game only 3.68% of the time.
That's the difference between theory and reality.
Try it yourself.
http://www.transtats.bts.gov/OT_Delay/OT_DelayCause1.asp?pn=1