Given the reason that airlines employ overselling, you would have to expect that it would impact the airline profitability, which could in theory lead to an increase in ticket prices. The bet SWA is making is that the revenue gain from overbooking is smaller than the consequential losses from bad publicity. Just think about the downside to United based on their share price alone, and now the increased focus that is on the 'good conduct' w.r.t bumping passengers in the light of it.
The maths of overbooking is that if you have 100 bookings on a 100 seater flight and 97 passengers show up then perhaps you could have sold 103 tickets and still not have to bump anyone. In this case you have increased revenue by 3% without an increase in costs. This can either manifest itself in an increased profit or, on a competitive route, lower ticket prices.
Of course, there will be variations in the number of people who show up and this can lead to more passengers arriving at the airport than there are seats on the plane. In this case, there is a cost to the airline, and perhaps in this big optimisation problem there are some airlines that see a bigger payoff in overbooking and bumping than avoiding overselling and minimising bumping.
I don't know about budget airlines, but full service you might expect somewhere in the region of 5% overselling. For budget, I would expect it to be higher as tickets are cheaper so passengers have less to lose by not showing up.
Nonetheless, even if it were a 1-2% increase in revenue, it would have a much higher impact on profitability. On a budget route, you could have $500 profit per flight, say a couple of dollars per passenger. Every extra ticket that gets sold that the airline doesn't have to pay costs for is a big deal, and part of the optimisations that allow airlines to offer lower fares.