It's not false logic. You don't tax companies on turnover. The UK supermarkets, at their pomp in the 90s, made 18% operating profit (before taxes and investment and the like). So a 22% turnover tax would have bankrupted them overnight.
They all make considerably less now, due to competition from the likes of Aldi/Lidl and the internet. And customers becoming less loyal.
Plus you need to have get-outs from some tax rules. Yes, our tax code is way too complex. But there are still some legit reasons. Because if you don't have rules, people will exploit that too. Any time you have similar items at different tax rates, you'll have abuses.
There will never be a perfect tax system. Because there are always people with an incentive to get round paying, and there are always people with good reason to be exempted. And sometimes theh first pretend to be the second, or manage to game the system to share in their benefit.