re: You mean... We'd have to actually.... ENFORCE border security?
Rather than exempt food housing and clothing I'd suggest that there be a baseline deduction per person. That way if someone really spends big bucks on housing or clothes they still pay taxes on the 'excess'. The poor pay nothing, until they have enough $ to consume over the baseline. They'd register and get a tax 'credit' at the start of the tax year so that they do not need cash up front. And yes, seting the baseline has to be in the hands of the 'evil' elected govt.
Notice that even illegal US residents pay taxes at this point of sale scheme. You buy you pay.