I'm not familiar with FairTax, only my own thoughts on the matter.
Perhaps income tax will always be the better solution, but it at least needs to drop the thousands of special interest exemptions. A deduction for missing an eyeball?
The only reason I suggest a federal sales tax is that it seems to be successful at the state level, considering most have it. If only 5 states favor an income tax over a sales tax, why would sales tax be preferred given the disadvantages you mention?