When researching my first hunt in 2014 all of the agents I talked to said the cost was the same whether I booked through them or directly with the outfitter. They would be paid the deposit and forward it to the outfitter and be the go between of anything went sideways. I didn’t ask how they were paid but I used them as I was new to booking international hunts. On my subsequent 4 trips I’ve done the booking myself but if I can ever afford a trip to a more exotic destination like Cameroon, Ethiopia or Uganda I will go the booking agent route.
When a booking agent screws up, they always point fingers at the other guy (operator) you didn't contract with. Many tales on this forum and elsewhere of people saying "give me my damned money back" to which the most noble of booking agents says "if I agree to surrender all funds I earned to you and call it a total loss, I can give you back 15% for the disastrous situation with your hunt".
There may be some areas of the world you cannot hunt without a booking agent, but they cost a lot and are indeed, commissioned sales people. If anyone has ever been in sales, you realize you must often sell products you don't really believe in. Caveat emptor with middle men that separate you from the ultimate recipient of your cash.