Not necessarily. In most cases, the venue (or wherever the offer money comes from) has the most pull. The middlemen, or the agents and talent buyers who bring the deal together are just filler. The venue (the decision-makers) and the agent (the product/act) are the two largest components of any entertainment deal. And it is important to remember that not every act will work well in every room.
Frequently, more time is wasted going back and forth waiting for the talent buyer and booking agent than it's worth. You may save $10,000 but you'll often lose $15,000 in tickets ales due to lost on sale time. When it works there is some benefit.