This can happen with any airline within the OW Transatlantic JV. I dread to think what the experience would be like if something went wrong with IB. Likewise, AA and AY’s call centres wait times can be lengthy and YMMV on how “smooth” the resolution might be, not withstanding the lottery as to the person you’ll get at the end of the phone or the customer assistance desk at the airport. You could do the “long way” (assuming you’re EU/UK based) and go with QR and have a far superior product, however even their ground and phone service is variable and can be a complete contrast to their excellence onboard. All in all, nothing’s perfect sadly. Conversely there are reports of many fantastic experiences with BA. Their Club Suite is undoubtedly the best J product amongst the OW JV carriers (bar AY’s new upcoming one, but can’t take that into account as it’s not been rolled out yet). Similarly AA’s priority baggage handling (if you have status and/or travelling in premium cabins) is superb and my bags have always arrived amongst the first few without fail in all my travels with them.
End of the day, anything can go wrong, I’d base my decision on the hard/soft product of the airline in question for the route you wish to do, the value of the redemption itself (ie. Good Avios value per pence), the lounge propositions available during that journey (eg. I’d choose airports that have AA’s Flagship lounges or an AS or BA lounge rather than Admirals Clubs) and lastly convenience. Good luck!