Booking directly will get you the best price nowadays on most airlines with just a couple of exceptions such as perhaps the legacy Japanese carriers or some airlines in China.

The reason to book through an agent would then be not for the lower price but if you can't get the same itinerary booked directly through the airline.

However, as @Non-NonRev pointed out, in case of any flight changes you'd be forced to deal with the same agent, who might be difficult to contact over the phone.

Unless the deal is very good, this extra layer of complexity is not worth it.