Yes most travel, certainly the less complex can be self booked online and self managed ...
However as mentioned it generally involves time researching elements from many sites and possibly inputing multiple fields repeatedly for each component.
Travel agents mostly utilise GDS booking systems which interface deep into many airline inventory systems and can therefore access a much higher level of data. Airline public web booking engines are basically designed to be used by "dummies" with a low level of access and very strict controls over inputs/outputs. Multiple sectors (air and land) across multiple carriers and suppliers can be booked in a single PNR via a GDS ... with stored personal profile info being transmitted to relevant suppliers ... FF numbers, seating and other preferences etc. Also when the **** hits the fan as in the recent Qantas grounding its good to have someone on the inside looking after your rebooking options etc, beats waiting in the phone holding pattern for xx_ amount of time. TA's will mostly also have comprehensive back office systems that are designed specifically for the management and accounting of travel bookings.
Most TA's these days operate within large buying and marketing groups, there are very few fully independant agents. These groups have much greater leverage than most end users even large corporates. And airlines, hotels, car rental groups and other suppliers usually have specific agency account managers to sort any issues. Most TA groups will have access to unpublished, nett and even privately negotiated fares at times. Most agency groups have specialist "fares" desks staffed by airfare experts who spend their days working out the best options on complex routings. Agency groups will generally also have access to hotel deals and at times have allocations of rooms which can be very beneficial when demand is high.
Agents by and large work for relatively low rates of remuneration vs the knowledge and complexity of the tasks they perform. Yes they are paid commissions on some products and this was tradionally the way agents earnt their revenue. Over the past decade this has been changing and many suppliers are squeezing or eliminating commission payments and many agents will now charge fees for service. Generally the fees they charge will be offset by what they will save by being able to access better priced travel products and by saving you the time trying to find it all and piece it together.
But having said that many travellers enjoy the research and planning themselves and many are happy to and capable of managing their own travel arrangments. There is no right or wrong, yes or no answer, its really a case of summing up your own travel needs and deciding what will work best for you and your circumstances.