Idk the specifics of the court mechanics and all that.
I know that blind birthright citizenship is a bit stupid, personally. You need at least 1 additional condition to have the baby be a citizen. For instance, having at least 1 parent who's a long-term resident of the US and has paid taxes would make sense. Alternatively, having blood of a US citizen even if they currently don't reside long-term in US could be a justification.
Either way, to unconditionally give birthright citizenship doesn't make much sense to me. It basically allows enemies to pop over to US, have a baby and then their offspring are full citizens from birth based on no other factor than that. From that point, you've basically only screened the parents enough that you know they aren't a known enemy of US. However, here's where it gets really problematic.
So, let's say you had a known foreign criminal woman and her forgeign husband even more so, they're in US. They are under arrest or detained and have a baby. That baby is now a full citizen of US despite the parents being known criminals, having no loyalty to US at all nor residing there anything close to long-term.
Birthright Citizenship as a flat concept is flawed. It needs to be conditional. What's really interesting is nearly the whole world outside of the Americas (meaning outside North and South America both) don't have birthright citizenship how they do.
Online sources seem ignorant of a few exceptions in Africa as well as Pakistan which uniquely, for Asia, offers unconditional Birthright Citizenship (but it has 1 condition, the father can't be a known enemy of Pakistan, that's the only real condition it has).
The approach of 'born here, okay, you are a citizen' is overall specific to the Americas. Part of why it may be a trait inherent to the Americas is they're founded on invaders feeling indigenous to the land. However, this doesn't explain why Australasia doesn't have this policy.