As an American who has lived abroad a fair bit, I can confirm that the American approach seems deranged if you're used to prices that match what you will pay.
But the problem is that right now a supermarket chain can advertise in the newspaper that chicken breasts are $4.99/lb at all of its nearby locations.
If sales tax were included, you couldn't advertise prices at all, because they might be different at each store!
How could Apple advertise the price of a MacBook, when sales tax is 0% in New Hampshire, but 8.875% in New York City, but 4.5% in Yonkers just north of NYC? That's a price variation of around $100–200.
That may not be super sensible, but it is how it works. A business on one side of the street may have to collect taxes at a much different rate compared to a business on the other side of the street.
You already have to produce different ads in Spanish, Italian, German, etc. So it's not really any extra work to have different prices in each.
Plus you're only dealing with tens of countries. There are literally thousands of distinct sales tax geographical areas in the US.
Attempting to maintain the same final prices in one town with 3% sales tax and a neighboring one with 8% sales tax simply isn't workable.
I mean, sometimes it's fine for extremely high-margin electronics, or things like cell phone service where marginal costs are low, but it's definitely not the case in general.
Individual items can have >100% markup, there are items sold at a loss to ensure you can complete your trip at a single store or get you in the door or whatever, and the store absolutely has to consider how revenue (not just line-item profit) plays into things to balance out rent and wages and whatnot. 1-3% profits for the store don't imply much about what you need to charge to offset the effects of sales tax.
As a brief example of irrationality, last I checked, on like-new iPhones it made a 30% difference in total revenue to offer "free" shipping rather than split it out as a separate line item. People would really rather pay 1.3x with "free" shipping than 0.8x base price and 0.2x shipping.
Somehow this all works magically here but in the US it is impossible because.. reasons unknown
You're drawing an unwarranted conclusion that just because not all prices are coordinated, therefore none must be.
If you consider that, I believe your reasons unknown become reasons known. No need to resort to magical thinking :)