Systems are built on human behavior. Humans who spend entire lives looking for ways to exploit system. The above system was tried, and indeed got exploited for luxury in a big way.
To some extent I agree to the income tax idea. But you're far too extreme. Income tax makes jobs possible or impossible. The lower it is, the more occupations are realistic to have. So we should have a rule for governments: if unemployment is above, say, 4%, income tax must go down until unemployment drops below that 4%. If unemployment is below 2%, income tax should rise, and the state should be forced to deal with the lost income. This probably isn't a good rule as stated, but something along these lines would be good.