You've skipped addressing the adoption analogy. In an adoption the same termination of parental rights and duties occurs yet people who give up a kid for adoption don't face this. What is so distinguishable to make it acceptable to bill bio-parent Here?
The difference is that an adoption contract doesn't have two parties, it has three: The birth parents, the adopting parents, and the state. The state is involved in the process, and will only allow adoption if the adopters can demonstrate financial security. In the sperm donor case, there were only two private parties, and their private agreement should not be able to force an expense onto the taxpayers.