I was wondering this too. Maybe due to the extensive time it took to get this done, they don't want to tie up the phone agent for an extended period. However, if that was the only reason, then I think they would just be directed to tell people to use chat. I am assuming the chat agent is able to help more than one person at a time. He would chat me every 8-10 minutes to say they were still working on it. He first had to wait in a queue on his end for whatever Oneworld support he was using. He didn't call it BA support, he called it Oneworld support.

I surely hope the airport agent wouldn't have needed to take an hour to change it! I am glad I got it done ahead of time from my office, and I didn't need to pay to park.

I've also considered that the phone agent just didn't want to deal with it if it takes an hour! LOL