I have to say, for anything other than a straight BNE-LAX return (for example), I have used a TA. I too have had plenty of problems and it's so good being able to call the TA and get a little help, someone else who is away from the chaos (and customer service counter with the hundreds or thousands of others trying to get their problems fixed).
I have been stuck in Hong Kong before, just in transit and found that my ongoing flight was full and I was not longer on it
I was only 17 then and flying by myself. It was great being able to call home, have the TA work her magic, tell me what counter to go to and voila, I was on the flight. Also arriving in LAX once with delay and cancellation dramas, put up in an airport hilton by AA and being able to call home, get my TA to reorganise our return flights to avoid the same problem. The list goes on.
I can not tell you how many times our flight number and departure have changed over the years particularly on a Vienna - Geneva flight ret that we have taken many years in a row. Every time it changed, which seemed to be almost weekly, my TA would call me, then email through the details over the months and even whilst away.
So whilst I'm not for TA's in Australia to book Disney accommodation (actually my TA would not book that for me once when I asked about it, she told me it was cheaper to go direct years ago when I organised my first adult Disney vacation), I am for TA's for booking flights that are anything other than one over and one back. You are still booking direct with the airline or airlines, but you have someone else to sit on the phone and do the leg work if there is a problem or any changes. My TA is a corporate agent, not one in a regular retail TA