I agree with your premise because this seems to be the modern interpretation of the courts, but it is not the historical interpretation.

The historical basis of the bill of rights is that they are god given rights of all people merely recognized by the government. This is also partially why all rights in the BoR are granted to 'people' instead of 'citizens.'

Of course this all does get very confusing. Because the 4th amendment does generally apply to people, while the 2nd amendment magically people gets interpreted as some mumbo-jumbo people of the 'political community' (Heller) even though from the founding until the mid 1800s ~most people it protected who kept and bore arms didn't even bother to get citizenship or become part of the 'political community'.

There have been cases of illegal immigrants demanding 2nd amendment rights and getting them ever since it was incorporated to the states in McDonald