For unrestricted tickets, SWA charges less for children 2-11 years old than for adults (defined as age 12 and up, as opposed to the usual definition of 2 and up). And their unrestricted adult fares are already lower than other airlines. Somehow this doesn't put them out of business.

Now, when you look at restricted fares, which is what most passengers buy, especially families, SWA does not have a lower fare for kids.

I think the reason you don't see lower restricted fares for kids is because restricted fares are already below average cost. Also, load factors are very high, so there aren't extra seats to sell at a discount to a family of four rather than a single traveller (paying the same fare per person).