Many companies like orderly processes to save overhead.

Where I work, to purchase something I'd have to get the approval of my boss, involve the purchasing department, possibly get three separate bids by different vendors if the amount is high enough, select the best (not necessarily cheapest) bid, send the invoice to accounting, etc.

The total could be several hours of working time. The cost of this time is much higher than just my salary, there are taxes, rent on the office space I use, and so on.

If the vendor has been pre-selected, the process is much easier. Get the expense approved by the boss, tell the purchasing department, and they'll place the order. This can save several hours.

A corporate travel agency, or nowadays, a "travel management company," can provide a number of benefits:

• Control: everything goes through one central source. The agency can enforce corporate travel policies, so nobody has to worry that you've gone off and booked a ridiculously expensive first class ticket or added an unauthorized 3-day stopover in Aruba to your itinerary. They don't want you booking a ticket that costs $1,000 more just because you want the frequent flyer miles from that airline. The agency can evaluate the price/time options for flights and recommend those toward the cheaper end of the spectrum, or require appropriate approvals for more expensive travel. They can also check for airfare price drops after booking and ensure refunds or credits are handled for cancelled trips.
• Payment: everything is billed centrally, and the finance department only has to deal with the approved travel that's been submitted by the agency. Employees don't put travel on personal credit cards, nor does the company have to issue corporate cards to everyone.
• Time and skills : not everyone is good at booking travel (some people are terrible) and companies don't want their employees spending large amounts of time comparing options when there are professionals to do the job. Not every employee knows to use websites to compare fares from different airlines or to search for flights from different nearby airports. Of course, this can be frustrating if you do know what you're doing and don't like the options the agency has given you.
• Changes: the agency gives you a 24/7 number you can call to make any changes, and late-minute changes are a common need with business travel, instead of dealing with the airlines. Any change fees can be handled through the agency.
• Discounts: businesses can maintain relationships with airlines, hotel chains, and rental car companies to get discounts and perks in exchange for their business. These range from programs for small businesses like United's PerksPlus to a large company or two buying up enough business class seats to convince an airline to operate an entire longhaul route (gestures at Swiss's "Roche Coach", an SFO-ZRH route for which Roche's commitments were reportedly instrumental). A corporate travel agency will manage these agreements and direct travelers to the best fares for the company, including non-public negotiated deals.
• Awareness of where everyone is: the agency maintains records of all employee travel, so the company knows where all employees are in the world and can respond to any emergencies.
• Events: want to fly a candidate out for a job interview? Or need to fly 500 customers half way around the world to an event? An agency can do that, handle all the logistics, and manage the billing. It would take in-house staff time to do the same.
• Reporting: the agency knows the entire business's travel patterns, and can produce reports to help find ways to reduce expenses.

Whether the company is actually getting their money's worth is harder to evaluate. Processing an expense report costs money, so front-loading more of the work onto a travel agency takes some work off of the finance department. Stopping just one employee from wasting money on unnecessary travel expenditures can add up to a lot of $45 booking fees. Or perhaps they're wasting their money and would be better off without the agency. Travel can make up a large portion of a company's budget, so they may find the part of the process that you don't see, the behind the scenes management of the entire business's travel, to be worth the cost even if it doesn't seem worthwhile at the individual booking level.