Because most natually born citizens do not renounce
citzenship so that birth certificate can be used
to enter USA and establish work eligibility.

and also local government etc do not keep a list of
names of those who renlouince citizenship. Dept of state
keeps such a list so that they will not still
issue passports to these people.

But tax is different. Citizen or nor you
have to pay taxes on income earned in USA.
To use offshore bansk, both citizen and non-citizen
can do that.