firstly, you dont pay an agent. an agents fee is generally charged to the promoter on top of your fee (thats how its always worked with i agencies i've booked artists from), so the agent only gets paid if you're getting work which drives them to find work for you.
theres a number of reasons for using an agent.
1. time constraints (jobs, kids, studio work etc etc)
2. contacts
3. language barrier
4. business know hoh (not everyone has a head for negotiating fees etc)
thats just a few that apply to me and im sure theres plenty more.