Lower surgery should never be required to change your gender marker.
That would not be ethical for many reasons, not the least of which is the fact that some people cannot physically undergo a surgical procedure. Their body isn't strong enough or healthy enough for it, and preventing them from changing their gender marker due to a physical limitation is a violation of the disability acts.
Not only that, but if you really want to require a penis for 'malehood' and a vagina for 'femalehood' then what in the world do we do with cisgender men who lose their penises? If female were default we could 'force' them to be listed as women, but then that means any MtF doesn't need bottom surgery, since a vagina wouldn't be a requirement of being listed as female.
This creates the conundrum of 'sexless' people. Would they get all forms of government I.D. taken away from them? Would they create a new category of 'neuter' for those who have no sexual organs?
After all, if a vagina is required to be listed as female, even a man who lost his 'legal right' to be male through injury would still not have the 'legal right' to be female.
The entire idea of requiring surgery is bogus, insane, and simply doesn't work in theory. There are too many situations where it falls apart.
And really, the government is worried about people 'hopping' gender? That's not going to do a dang thing. That's not going to cause trouble even if people were doing it. People who want to evade a crime need only to get a 'fresh' social security number and name, they're not going to live as the other sex. They don't NEED to. After all, there are billions of people in the world, it's not like someone's going to say, "That's a man, so he must be ______."
Good grief.