By not paying Income Taxes though, the bar for entry is presumably lowered, making room for more competition in that market. Assuming capitalist principles still apply, it's a race to the bottom on prices, and the vendor who provides the best service for the lowest cost wins.
This isn't quite correct. What happens with the Fair Tax is you get a monthly "prebate" from the Government, which is based on the Federal Poverty Level. This means, you're still paying the taxes at the retailer, but the Government has already given you the funds to pay for those taxes, so it "balances out". If you spend money on necessities at a retailer, which goes above what the Government deems to be your basic needs, then you're still paying Sales Taxes.
Her son dying. Not kidding.