“…when that fuzzy diving line is crossed”
I think there are circumstances when the line is clear. If your child is born in the US, you’re an American. If you’ve held down a job for a decade, you’re an American. If you belong to and donate to a church that actively supports its broader community, you’re an American. If you love the Never Ending Pasta Bowl at Olive Garden, you’re an American.
Not legally, but spiritually.
I think the problem is that amending the constitution is too hard.
Many states have an amendment process involving ballot measures, where a supermajority of voters can amend the constitution. This is not without its problems, but amendments pass more often, and it has the attractive aspect of directly consulting the citizenry.