I think if you look at the numbers, as NC already pointed out, you will find that CX is already what some people call an LCC. The only difference between us and some LCCs is that we offer full service and assigned seating.
What people don't realize is that the readon CX is so efficient is the high aircraft utilization rate. Before 9/11, a lot of US airlines were just run really sloppy (Some still haven't got their act together). SWA didn't change much after 9/11, but other airlines did and they really tightened up their ops. Before 9/11 some legacy carriers in the States were getting as low as 8 to 9 hours utilization per day out of their aircraft. They have all increased these figures to approximately 12 to 14 hours since then.
CXs utilization is pretty high and only gets higher. I have rarely gotten off an airplane that sit for more than a couple hours in Honkers. Transit times in other ports are even lower. Now, some people will say (me included) that this is taking a toll on the planes. But, it still menas that CX has lower costs than carriers who fly their planes less.