Interesting ... I've encoutered the opposite (excellent service in making ticket changes and no hassles, even for complex and difficult changes ... while you have unacceptable service for a trivial change). The SIN problem I can understand, most likely it isn't CX staff but contracted and they are overly rigid (you have to get the station manager and then anything can be done).
My changes went as follows: Before boarding my flight to HKG I ask CX to send a message that I wish to make a ticketing change. I wrote out the changes on a sheet of paper while I was inflight to HKG (thanks to the CX downloadable OW timetable I had all the flight numbers and times perfect). Upon arrival I am met at the plane and taken to The Wing (the ticketing desk is outside in the A section of check-in). I gave them the sheet of paper and my ticket and explained my changes. Then I went to a cabana while they went to work. An hour later it is time for my connecting flight; they phone and say they have trouble calculating the fare and it won't be ready in time, but they will meet me at the gate for my next flight. Later I go down to the gate and wait. The gate is expecting me to board at the last minute, not a problem. The agent runs up, gives my old ticket back, with the first 2 segments stickered. Apologizes profusely, says please use the old ticket for now (so I don't miss my flight) and when I return to HKG they will have my ticket ready for pickup and I can exchange the old ticket for it and make the additional collection payment. No problem that my next 2 flight coupons don't actually match what I am flying (they are stickered), or that I owe money. When I get back to HKG, agent meets me at the plane and asks if I know how to go to the ticketing counter (I am not in transit this time). I say yes, refuse their offer to escort me, and when I get to the counter my ticket is pre-printed, I pay and exchange the old ticket. Total time 1 minute. Check ticket, all changes exactly as I requested.
I have no CX status but I fly them a fair bit and some of the staff recognize me so maybe I am getting special treatment (I don't think so). I went into great detail on this description because I was surprised to be met at the plane both times and I was impressed that they were willing to trust me with the old ticket (in another city) while they issued the new one. I could have lost the old ticket, or cashed it in, causing lots of problems for them; but they valued my time more highly than their convenience. I can't imagine AA doing this -- you have to stand at the ticket counter, for hours, while they do simpler changes.