If what they say is to be believed, then their execs don't understand their customers.
According to CNN, they started selling on flight finder websites and didn't see the expected increase in sales, and assumed it was because people preferred cheaper flights and to pay for their bags.
In reality, there's no increase in sales because the "good luck sitting next to your family" plan doesn't work for a lot of people, and most of those people avoid Southwest like the plague because of the nickel-and-diming upcharges just to have a chance of sitting together. As long as Southwest hasn't implemented reserved seating, and requires people to pay money to avoid a panicked rush 24 hours before the flight, when the people who are the least able to take the time to do that (people with families) are the most heavily impacted by the policy, then Southwest isn't even an option.
Besides, I guarantee Southwest isn't going to meaningfully lower their rates in exchange for not bringing checked bags. Every airline that has done this has ended up with longer boarding times and everybody bringing their bags and then gate checking them anyway when the plane ends up being full, which delays departure even more, but you'll notice that the prices on those airlines are still higher than Southwest, because most of the cost of air travel isn't the 60 checked bags weighing less than 50 pounds each. A 737 weighs 140,000 pounds. Those 3,000 pounds represent O(2%) of the cost of the flight. And I guarantee they aren't going to charge only $3 per flight for a checked bag.
No, they're not doing this to lower prices. They're doing this to encourage people to bring less luggage so that they have more room to carry mail and make a bigger profit on each flight . And that's fine, but it would be nice if they were at least honest about it.