IMO, a fickle client is one that wastes the agent's time. However, unless you have a formal Buyer's Agent agreement, you are free to use whomever you want.
You should have an agent who is reasonably accessible and shows you only what you specify your wants are. Anything else is a waste of time. Your agent of choice should also be skillful in negotiation & working the deal to a successful close after the contract has been agreed to. It isn't about just finding the appropriate property.
We usually work with a team of agents & it is important to be comfortable with them all, but there's always one lead person who should be very experienced, i.e. successful. If one subs for the other, they work out how to split their commission, if necessary.