I love this idea! However, I think that unfortunately this argument doesn't hold up, and wouldn't in court. The information is available via their site, but that does not make it public.
If the info is on the web it's available to be consumed by humans or robots in a polite manner.
Data wants to be free.
Them trying to enforce their terms is another matter. Maybe it would hold up in court. Stupider things have. I mean they should start telling us how to breathe air next. Because ya know if it's in your terms then it must be legally binding.
Could one offer fair information if there's no reference to Southwest? Is having a website full of listings like "flightno: 123, flight_datetime: 2018-03-04-1045, price: 234.56, price_datetime: 2017-11-15-1130" something Southwest could successfully block?
There are conditions on their site, and most sites.
Separately, if this information was public, then Google would have already incorporated it into its flight price notifications feature.
But again, fun idea. It's a good example of something individuals could create for themselves, and Southwest would likely never notice.