Have you compared the amount of spend required to generate sufficient cash to buy tickets versus the amount required if you redeem for AAnytime awards? Bear in mind that AAnytime tickets are very flexible, while the lowest priced paid tickets are not.
I probably should have said cash-back or points card, because I've been seriously considering giving Chase Ultimate Rewards a shot. Being completely honest, I got into churning the Citi AA Platinum card solely for use on my trips to Maui from the East Coast. Now that I have to move our trips to peak travel time, I'm seeing virtually no availability of MileSAAver awards in any class, and AAnytime awards just seem too steep. For instance, this is what I'm looking at right now for travel next June:
Economy:
MileSAAver: 135k-187k miles total, but only 1 or 2 travel days per 3 months availability
AAnytime: 300k-420k miles total
First:
MileSAAver: 320k miles total, but only 1 or 2 travel days per 3 months availability
AAnytime: 540k-645k miles total
For my travel dates - which are never flexible - I'm looking at either 420k for economy or 645k for first. I'm averaging four Citi AA Platinum cards per year, so let's call it 240k miles on $12k spend (assuming I'm averaging 60k bonus miles per card), and then 23k miles/year based on an additional spend of $23k. In total, that's 263k miles/year on $35k spend. I'd be comfortable simply using miles to upgrade to first for these flights, as well, but since I have no status with AA, and because the Hawai'i routes are full, there never seems to be any award upgrade availability, let alone for a party of 3.
Conversely, I'd see the following:
Citi Double Cash: $700
Chase Freedom Unlimited: $525
Chase Sapphire Preferred: $525, or $656 when redeeming via the UR Travel Portal
I'm absolutely keeping one Citi AA Platinum card open forever for the free baggage alone, because even if I pay the AF, I still come out ahead. The CSP has a $95 AF, as well, so I can probably just knock that $656 down to $561.
Of course, after writing all of this, I decided to map out my mileage accumulation using the assumptions above [4 cards/year, $35k total spend annually], which is spoilered below. Redeeming AAnytime awards in economy seems like it would work for every single trip, saving about $3600 in total each time. I could even throw in a few first class trips without depleting my miles or being forced to buy additional miles to make up a difference.