This has not been the case for me. One of my best clients is a small agency that does not have an in house UX designer. They pass 100% of their UX work to me at the full price I decide. I had a very candid conversation with the owner and he was adamant about paying whatever to make me happy about the work to stay long term. It has been a win win relationship with them over the years. I charge a premium they are happy to pay and the work brings major wins for their clients which allows the agency to get even better and bigger contracts.