Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)

"Also all, or at least most, of the flight code shares with BA, it seemed purposely for this reason."

Nope. Codeshares are irrelevant for award travel. If a flight is operated by BA you can only redeem Aadvantage miles under the BA flight number, not under the AA (codeshare) flight number.

Award seats are more available on BA metal precisely because of the high surcharges. Many AAdvantage members would rather fly on AA metal with no surcharges, so those award seats get snapped up quickly.