Now that AA has merged with US, CLT is an AA hub, and AA is a oneworld alliance partner with both BA and QR and RJ.
But you haven't explained what your goals out of a loyalty program are.
For example, if you get to AA Gold, you'll have access to MCE at half price. Does that matter to you? You'll also have a chance at domestic upgrades (using 500-mile upgrades that we here call "stickers" for historical reasons), but the lowest chance on routes with a sizable number of elites with higher status. (I dunno whether CLT-SFO would be such a route or not.)
And are you using OW benefits? The problem is, if you stop putting in your BA FFP number when booking other OW international flights, you'll stop getting OW benefits. So why go to another program when you've reached BA Gold, if your'e never to go use those BA Gold benefits at that other program (you'll be starting from scratch). So the one and only case where I see that possibly mattering is going with AA to get domestic benefits which have nothing to do with OW Sapphire.