A flat tax seems to increase voluntary payment of the tax due, but may not decrease tax evasion, according to the Russian experiment begun in 2001.

And remember, most "tax loopholes" in the USA are not inadvertent... most are intentionally written into the tax law to encourage a social action thought beneficial by the lawmakers. e.g., low income housing credit, energy saving credit, employment of the unskilled, even purchase of a personal residence with borrowed money.