For a guy with a civilian airline background maybe but for a single pilot fighter guy, getting a type rating in a Boeing 737 versus a recip twin has numerous advantages.

1. Exposure to a civilian transport category training program.
2. Working with a co-pilot and refining CRM skills.
3. First real FAA checkride.
4. Brushing up on civilian regs.
5. Learning an aircraft that is relevant to airline operations.

Plus, its only a few thousand dollars more investment and the GI bill should cover some of it while the rest can be written off on your taxes. I've flown with 100s of guys who went through the weekend ATP program and didn't learn jack nor prepare them one iota for an airline job! If I were looking at a resume and the person had the initiative to get an initial ATP in a 737, all things being equal, I would hire him/her over someone who got it in a light recip twin. Why? They've demonstrated they can pass an airline training program to Captain standards.

As far as SWA goes, I thought they didn't require a type rating to get an interview anyway? None of the airlines are immune from pilots changing airlines and would be naive to think that pilots that don't have B737 on their license are there to stay!

Ultimately, its a personal choice and the pros and cons need to be weighed. Hence, this productive dialogue.