You are right. If ever there was a time, possibly now is the time. But, these justices are very reluctant to overturn long standing precedence over such a politically charged issue. Look how long it took them to hear a case over abortion rights - which was not that long standing in comparison as the birthright citizenship issue. With abortion they were able to correct what they felt was in error and kicked it back to the states to decide thus giving them an out. They were not scraping abortion rights - they merely shifted the responsibility back to the states where it should have been to begin with. This would be different. There is no shifting of jurisdiction here.

No doubt it would be a crap shoot because it would require the court to reinterpret the language of the amendment itself. IMO the odds of them hearing a case like that would be slim to none. But, I could be wrong. We would not know for sure unless someone could construct a Constitutionally sound argument that would allow them to take the matter up. The justices know all too well the impact of such cases and the blowback that comes with them.