This is a conjecture that as far as I know does not match what actually happens, which is that the new infrastructure is paid by debt, and the 4 new taxpayers will not have paid off the debt before the infrastructure needs replacement, paid for by more debt.
If it was 600 new units rather than 4, maybe it works out that the corresponding taxes pay for the infrastructure, but property taxes just aren't high enough, and the people who live in these boondoggle houses aren't wealthy enough to pay the taxes for the infrastructure their houses need