Unfortunately it appears that the concept of "caveat emptor" and self accountability, while endangered species during Generation X, has since become officially extinct.
As an expensive and important of a tool as we are lead to believe here, is it too much to ask to do your own homework? I travel with specialized sports equipment, not high value stuff in the grand scheme of things but over-sized/important/etc. The first thing I did was research how United was going to make my life difficult in the process. I've had no problems, because the rules and restrictions are published and freely available before I chose to do business with them.
AA's policy isn't even complicated. I found it via Google and read the policy in less than 5 minutes. It's essentially 3 bullet points and the 2nd one,
"Is a bulkhead (divider) window seat (not in an Emergency Exit row)"
is a gigantic red flag. Proceed accordingly. Yes this might mean you need to spend a few more minutes consideration to sort out your precious million dollar cello.
We don't have a transcript so nobody here knows how the call went down. What I think we can agree on is the $15/hour phone booking agent at AA didn't know any better. It would be naive to assume that every booking agent knows every last detail of an airlines policy. Many of these agents actually book for more than 1 airline. It's a possibility the agent has never even booked a cello let alone with AA before. It's unreasonable to expect the level of perfection and competency demanded in this thread out of what is basically one of the lowest rungs at the airline. This is a phone agent not a gate agent. Who books airfare on the phone anymore, anyway? (tongue in cheek, relax)
As for the policy..... it's there, established and was (eventually) correctly implemented which unfortunately resulted in 1 person being mildly inconvenienced. In an industry fraught with safety and risk-aversion as the number one priority -- fortunately it's not up to FAs/etc to choose when they feel like implementing official policy or not. AA's first screw up was actually allowing the cello on leg 1 (presuming it was also not booked in the proper seats) doesn't constitute a requirement for them to break policy on leg 2. Two wrongs don't make a right, etc, etc.
It was said before, the airline can never win when all of their employees aren't perfect little robots 100% of the time. Time to cattle call (no pun) the social media brigade! In a Monday morning quarterbacking world AA could/should/would have done all kinds of things "better."
I was hesitating to toss this out here but the "plays cello, ergo 4 times as educated as anyone here" comment got me good. Sooooo educated you can't book a plane ticket properly? Got it.