I'm a strong user of my TA for o/s travel; I book all my personal domestic stuff on line.
Most of my travel is to Nth America for a client, but about 30% is personal travel, involving western and eastern Europe, north Africa and Asia.
I began using the TA in 2003 originally because most of my o/s travel was for a new client, who used the TA (also for domestic). After a year I started using the TA for my personal o/s travel as well and haven't looked back. The TA is part of a medium sized firm in Melbourne, lots of corporate clients but also mums and dads as well. I wouldn't use one of the discounter, walk-in-off-the-street TAs.
1. Time saving. I do some preliminary research so I know what's basically out there, then get the TA to give me priced options, which get finessed etc (hotels as well as flights). I spend enough time away from home and I don't want to spend hours and hours of home time planning the next absence!
2. Cost saving. Whenever I have relatively 'plain vanilla' flights, I'll price them separately to compare with the TA price. There's never been a material price difference, and often the TA will come up with terrific savings. For instance the LH and AY Europe fares which include a QF first and final leg; not available on-line. Whenever I point out a material price difference (mostly happens with hotels) , if the TA can't match, then there is no problem in booking myself. You might say 'well, naturally' but if a TA has spent professional time getting prices (provided the service), there is a moral obligation to go with them. A good TA will say no worries (as mine does).
A good TA will not only advise the fare price, but also change and cancellation fees so that an apparent attractive fare can be seen in context wrt, say, a business trip, where schedule changes are likely.
When my TA has spent a lot of time researching a tricky personal itinerary and I ultimately don't travel, I always say 'please invoice me for time'. Never has happened.
3. Rescheduling of payments. If an advance fare is due to be paid by a certain date, the TA will automatically watch loadings and knows a fair bit about their trends for the major routes. TA will do a rolling re-book of the ticket until availability gets low, even holding dual bookings until the airline systems catch up (quickly, these days!). Delays my payment until absolutely necessary and keeps my options open for a better deal (or a DSC offer !) in the meantime. I guess I could do this through Expert Flyer, but risky if I don't check on a critical day, I'm stuffed. Plus the time again. TA does it automatically.
4. Assistance when things go pear-shaped. A real, 24/7 help line. If they booked it, they fix any issue.
Well, that was a bit of a love-in. But if you get a good TA, they save you heaps of time, and can save you money (beyond the value of your time). And if you don't want to use them for a particular trip or booking, then don't.