FairTaxers, themselves, recognize the potential for tax avoidance when they say their scheme restores freedom - you get to decide when and were to pay the tax. (or maybe you're reading avoidance as evasion?)
Economics is not just numbers, its human behavior. All those economic studies (paid for by the FairTax organization) are claiming that within a given set of circumstances, human beings will behave a certain way. For example, remove tax on earnings from investments, and human beings (wanting the best deal for themselves) will invest.
The FairTax organization passes over, or rationalizes away what those same people (wanting the best deal for themselves) will do when facing high taxes at the point of sale. They contradict themselves when predicting human behavior re taxation.
And you miss the point that with the FairTax the effective tax rate on purchases will be less than the effective income tax rate is presently. With that being the case people are even MORE likely to consume (as well as invest) hence the increased economic activity that the economic studies predict.