It's worth remembering that in the same way insurance comparison websites are acting in the same role as an insurance broker, many travel booking sites are actually "online travel agents" ("OTAs" in industry jargon).
To truly cut out the travel agent, you need to book directly with each supplier - the airline, the hotel owner, the local taxi firm, etc. Doing so may well save you money because agents and aggregators will often make their profit by adding commission. The most immediate cost will be in your time, and the increased risk that you don't sport an option that an agency would have offered you.
Beyond that, there is something of a spectrum of benefits that an agency might or might not offer:
- Exclusive deals with some suppliers that you can't access directly
- Personalised expert service, most valuable if you have unusual tastes or needs
- Bonding / protection schemes like ATOL, which offers you protection in the event of supplier failures, which you otherwise need to insure against yourself
- A contact number for someone who speaks your language and can help when something goes wrong
For a "bucket and spade" or "city break" holiday to a common destination, you might decide the travel agent doesn't offer enough value, and finding a low-cost flight and local hotel or apartment is fairly straight-forward. For a more unusual trip, such as an overseas walking tour or round-the-world trip, you might decide that a travel agent's expertise is still valuable.