My choice (don't laugh) would be AA for your transcons and midwest flights and WN for your short hops between SoCal and Vegas.

AA has nonstops to NYC and STL. Everybody has one-stops to Omaha so you aren't losing anything by flying AA there.

WN has SoCal to Vegas covered with dozens of flights, and the segment is so short that the service on EVERY airline is going to be pretty much the same. WN isn't too popular on this board, but as a complement the bulk of your travels on AA, it's not bad.

It's easy to collect lots of WN credits if you rent cars, so a few Vegas trips will put you at a free ticket, whereas it might otherwise only put you at a few thousand US miles. Last year I flew maybe 3 total roundtrips on WN, but rented about 15 cars and ended up with over 2 free WN tickets. Right now Omaha is too cheap to use awards, but six months from now it could easily be a place nobody is running fare sales to. All of a sudden those WN freebies are looking pretty good.

In general, I'd pick 1 legacy carrier and consider Southwest. I probably wouldn't split between 2 or 3 legacies unless you're really flying some odd routes. The key with the legacies is making it to that first elite tier as fast as possible, so splitting among several of them will just end up with you hating them all. You will hate flying the legacies until you reach the low-elite point, at which point it begins to become more of a humane experience. If you can hit mid-tier on AA, it then becomes a relatively pleasant. Not as good as it should be, but tolerable.