But the contributions to the economy from illegal aliens will not be taxed under either system.
I agree that nannies and yard crews (and other cash-pay work done by illegals) don't currently pay income tax today. But they won't collect and remit sales taxes under a sales tax. The big difference between you and me is that you think a sales tax will capture the economic contributions of illegals. As I have said, there is no activity that a sales tax can capture that an income tax can't.
We both agree that the consumption of illegals is taxed today through so-called "embedded taxes". Consumption of illegals in the legal economy will continue to be taxed under a sales tax regime.
"Consumption of illegals in the legal economy will continue to be taxed under a sales tax regime."
Agreed. It is simply a matter of whether they are given a tax preference or a tax disadvantage, not that they are tax-free under one system and taxed under the other.