Why? Airline-specific cards are actually not the best way of earning frequent flyer miles (apart from the sign-up bonus), as generally they only earn bonused spend on airline ticket purchases - all other spend is at 1x. Most people get airline cards just for the signup bonuses, and then cancel them before the annual fee becomes due. Right now, most of the cards (with the exception of the ones offered by Chase and AmEx) are still churnable. Some folks do keep the cards open long-term for the benefits, but before doing so it pays to do some back-of-the-envelope math and see if the cost of paying for the benefits exceeds the annual card fee.

Too bad, because the combination of Chase Freedom and Chase Sapphire Preferred (and if you qualify for a business card, Chase Ink Plus or Ink Bold) is one of the best points- earning combos out there. Chase Ultimate Rewards points transfer to United, Southwest, and also Amtrak (so you may not need that Amtrak Mastercard you currently have). Chase Freedom is a no annual fee card which earns 5x points on rotating quarterly bonus categories, while Chase Sapphire Preferred (2x on dining and travel) and the Chase Ink cards (5x on telecommunications (cable, cell phone, internet bills), 5x on office supplies (gift cards!), and 2x on gas) have a $95/year fee.

You might also look at the AmEx Everyday, which is a no annual fee card which earns transferable Membership Rewards points that you can use with the British Airways frequent flyer program to book flights on American Airlines. But if you're interested in this card (or it's annual-fee big brother AmEx Everyday Preferred) get it AFTER you sign up for the AmEx Platinum Card the next time the Platinum Card offers a large signup bonus. You can earn as many as 100,000 points from a Platinum Card signup bonus. AmEx is getting stingy about offering more than one Membership Rewards signup bonus per customer, so it pays to go for the biggest one possible. Sign up for the Platinum Card and get the big signup bonus, then six months or so later, sign up for the AmEx Everyday or EveryDay Preferred and link it to your Membership Rewards account. Then when the $450/year annual fee comes due on the Platinum Card, cancel it. The AmEx Everyday or Everyday Preferred card will keep your Membership Rewards points from the Platinum Card signup bonus from expiring (and they are both nice gas and groceries cards in their own right).

You're not going to get that unless you fly enough on one airline to earn status on it (which from your #2 comment says, you won't).

From everything you've said, I'd suggest opening frequent flyer accounts with American Airlines, United Airlines, Southwest, British Airways (if you want to earn AmEx points), and Alaska (for those times you fly Delta on a paid ticket - Alaska has a much better frequent flyer program in terms of usability than Delta's). For earning American miles, the combo of the Citibank AA card and the AmEx Starwood Preferred Guest card works well - get the AA card for the signup bonus (and cancel it after a year, then reopen it 24 months later for another signup bonus) and use the Starwood card as your everyday spend card. For United, get the Chase United Airlines Mileage Plus card for the signup bonus (but cancel it after a year), and use the combination of Chase Freedom, Sapphire Preferred, and Ink Bold/Plus to earn Ultimate Rewards points to transfer to United, Southwest, and Amtrak. You can also look at getting the Southwest card for its signup bonus - but again, this isn't a card to keep long-term. The Chase Ultimate Rewards cards are MUCH better for earning Southwest miles long-term!