Of course profits are affected by tax. Tax impacts the ultimate sales price that can be levied.
I'll agree with that, but only to the point that it is an impact on the price that the purchaser will bear. By replacing an income tax with a sales tax, people will have far more disposable income (not having FICA taxes or income taxes deducted from their income), which also needs to be factored into the mix. The tax on the final purchase is also offset, in whole or in part, by the savings throughout the chain of production due to the removal of income and payroll taxes.
Don't make the mistake of assuming that prices under an NRST are today's prices plus the NRST rate -- you have to remember that a significant percentage of the price you pay today (and correspondingly, the prices that are paid at each stage of the production chain) is a result of the income tax.