A tax on sales is more regressive than a tax on profits
It wouldn't quite be the same thing as VAT, but we do have this exact same thing in the US except we collect the tax at time of purchase. I think you'd find many companies - and 100% of those in a high turnover low margin business like groceries - would simply tack the 22% tax on at the time of purchase. What do you think would happen to the price of an iPhone or Galaxy S, for instance?
Most of those reading this would not really be affected by a 22% tax added to their grocery bill, but those down near the bottom of the economic ladder sure would. You'd be taking a tax on profits, which is more progressive as the burden is shared between customers and owners, and replace it with a tax that would be paid by customers to a much larger degree.