Another side benefit of taxing the states is that the states can each come up with different plans. I think in some states they will keep an income tax. Others will try other forms of taxation like property taxes, or sales taxes. Still others will come up with something new.
In any case the states can decide what works best for them, poitically and financially. States will be able to use their tax code as a lure for businesses.
The problem with each state choosing a different method of taxation is that some states are small enough geographically for people to cheat.
Live in a state that relies on Sales Taxes but do all your shopping in the state next door that relies on Property Taxes or Income Taxes.
People near borders already do this over a measely 7% Sales Tax, and states are banding together to track down mailorder and internet sales taxes to recoup a relatively small tax rate. With a combined 30% Sales Tax necessary to satisfy both state and federal revenue needs, this evasion would be endemic.
You would need draconian enforcement and tracking with such large differences between states.
The FairTax, in contrast, requires no tracking because it is universal across all states and virtually all goods and services. The goods and services are flagged as taxable or not, regardless of who buys them. Only a deferment of tax for resale or as a business input needs to be tracked. Much less invasive and easier to administer.