When you sign a non-compete, it will clearly state that you can't work for a client you had through the agency for either a specific period of time, which will hold up in court, or a specific demographic area, which does not hold up in court. For instance, say you work with a nice family and they would like to always have you as a nurse, if they leave the company and hire you to work for them,, the company can sue and win for losses of income you have caused by taking their client.
I would almost agree that signing one is foolish but I also think it is unethical when people hire on at agencies specifically to find clients to steal.
There are plenty of patients out there for everyone to have enough. I am tired of back biting on anyone's part. That is why the agency is so nice for a change.