First, even if you were right about the medical part, "getting sterilized" is not the end goal of anyone transitioning, the end goal is feeling more comfortable on their own bodies, some of them might accept losing reproductive capabilities as a trade of, but not necessarily all.
Second, "trans" is applied to anyone that is not comfortable with their assigned gender at birth -not only to people that have gone through the full transition-, transgender people can fell comfortable enough at any point of the transition and many stop before the reassignment surgery (if you ever see a video of how it works, you might understand why). That means that many transgender people have full reproductive capabilities, and many want to have them, as reproducing is part of their goals/desires/dreams; same a many cisgender people, you see?
Last but not least, it is their fucking body, the government should not in any way be allowed to decide that one group of people should not reproduce, and force them to undergo medical treatment just due to pure bigotry, period.
Haven't you read all those concerned emails? OP's web design is great! 😂