"a flat rate of tax is very popular amongst" SOME "economists"
Companies have already a flat rate in most places. Income taxes are a different thing and it's quite impossible to keep a welfare state alive with a flat tax unless that's so high low income people won't be left much money. And even with a low flat rate tax most low income people won't be able to afford services a State won't be able to offer anymore - unless it has other sources of income (oil, gas, etc.) - as long as those resources are State-owned.