Giving a real estate agent the "exclusive right to sell" your property does not mean that there will not be other agents involved. Your agent is the listing agent and the most important part of his or her job is to market your home to other agents who work with buyers. Those agents will show your home to their clients. Regardless of who sells the home, even if you sell it yourself to a friend at work, your listing agent will earn a commission.
If you want full service from an an agent and his or her company, this is probably the only type of listing they will accept. Full service means an agent will advertise your home, place it in the Multiple Listing Service, market the home to other agents, and perhaps even hold open houses. This requires an expenditure of both time and money.
Only with an "exclusive right to sell" does an agent have a realistic expectation of earning anything on their investment in selling your home. That is why it is the most common type of listing.
Of course, the agent and their company still have to perform in order to get paid -- your home has to sell.
