ITA software might be "neutral", but it omits certain carriers that don't supply fare rules to it, excluding many low cost carriers, for instance. As such, I can beat it without trying very hard simply by going to direct to the websites of the likes of Ryanair or AirAsia if I know they're operating on a particular route, which is a shame, because I like their interface. Or, in this instance, Southwest.
Some of the travel sites using ITA's QPX API to drive their booking engine get prices from these other airlines via direct feeds or web scraping, but as pointed out here, they can be quite selective in what they're willing or able to show
It's still ludicrously easy to trip up the flight comparison services up with edge cases like the short domestic Yangon-Mandalay route, where ITA finds nothing, most booking engines offer ridiculously expensive flights connecting in China or Bangkok, whilst Innovata Quicktrip (which you should use when you're convinced there are direct flights the big sites aren't showing you) shows multiple direct flights a day with 6 different local airlines, provided you don't mind their clumsy twentieth century booking operations.
TLDR: Use Quicktrip (which doesn't give direct prices) to check if there are budget airlines or local airlines also flying on direct routes that the big search sites might not be showing, and try these unlisted airlines' websites direct if they seem more promising.
Some of the travel sites using ITA's QPX API to drive their booking engine get prices from these other airlines via direct feeds or web scraping, but as pointed out here, they can be quite selective in what they're willing or able to show
It's still ludicrously easy to trip up the flight comparison services up with edge cases like the short domestic Yangon-Mandalay route, where ITA finds nothing, most booking engines offer ridiculously expensive flights connecting in China or Bangkok, whilst Innovata Quicktrip (which you should use when you're convinced there are direct flights the big sites aren't showing you) shows multiple direct flights a day with 6 different local airlines, provided you don't mind their clumsy twentieth century booking operations.
TLDR: Use Quicktrip (which doesn't give direct prices) to check if there are budget airlines or local airlines also flying on direct routes that the big search sites might not be showing, and try these unlisted airlines' websites direct if they seem more promising.