What's misleading is that the advertised price should be equal to the amount of money that you have to pay for it. Where that money ultimately goes is irrelevant when you're calculating the costs to you. Using your logic they may as well just display the business' markup, and say "oh no, the rest of the price is the wholesale price, we're not charging you, just collecting it on behalf of them, like the taxes on behalf of the government."
Obviously the amount of taxes ought to be shown on the receipt for businesses with input credits and for general information, but the pre-tax price isn't the main consideration when you're actually making a purchase, as demonstrated by the grandparent's complaint re: airline pricing.