The main issue I see for those who look at a shared "spirit" is they don't want to enforce that spirit.
America is a nation built on common values!
So does that mean the government can test for those values and deny/strip citizenship from people who don't have them?
...no of course not!
So you're left in a situation where you can't even attempt to ensure the continuation of the basis upon which you're claiming your nation is built. It's like starting a business making widgets and being unable to hire and fire people based on their ability or desire to make widgets. Assuming such a business survives at all, you'll have no way of knowing whether or not it'll still be making widgets in the long-term.
The main issue I see for those who look at a shared "spirit" is they don't want to enforce that spirit.
So you're left in a situation where you can't even attempt to ensure the continuation of the basis upon which you're claiming your nation is built. It's like starting a business making widgets and being unable to hire and fire people based on their ability or desire to make widgets. Assuming such a business survives at all, you'll have no way of knowing whether or not it'll still be making widgets in the long-term.