The main benefit is the ATOL/ABTA protection of what becomes a "package" holiday if the travel agent puts it all together, rather than you "buying" things separately such as separate flights, direct hotel bookings, direct taxi/hire car bookings, etc., and they also tend to check you have adequate travel insurance (different needs for different types of holiday).
We've tried a few times to compare doing it ourselves against a travel agent putting it together and prices usually come out similar, usually the travel agent costs more overall, but not by too much really.
Having said that, we've not actually booked via a travel agent for over 25 years! Even before the internet took off, we'd moved over to DIY via phone bookings. As I say, we've tried since, particularly for "problematic" holidays such as a cruise that needed a very long taxi transfer and flights to/from different airports, but the travel agent couldn't put anything together better than we could ourselves (in fact re the cruise, their suggested itinery was a lot less convenient).
Going back further, we used a variety of "High Street" chains and independents. The chains were mostly awful with young disinterested staff who barely knew what they were doing, just looking at the computer screen and trotting out what was available - no "tailoring" at all. Once we were handed tickets to the wrong country (same name of town's airport but completely different country and airport code) - thank goodness we noticed it as soon as they handed over the air tickets, and we made them change it all at their cost - it involved A LOT of changes, i.e. dates etc as there were no flights to the correct airport to match our hotel bookings, so they had to change the hotel dates too, and the hire car, etc etc.
The independents were a lot better every time - they seemed to have staff who were more knowledgeable and weren't as dependant upon what they could see on the screen - far more competent and confident to make tailored itineries and book directly for each aspect rather than the "chain store" mentality of just telling you what packages were "on the shelf". We used to use independent "specialists" for golf and skiing holidays back in the day which worked well when there was no internet to do it ourselves.