I mean, it certainly does seem that way.

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.

Fair point on the advertising. Perhaps a good compromise would be to mandate displaying the price with the taxes included in store/on the website so what you see is what you get when you checkout with no bad surprises.

VAT rates in Europe differ too but it doesn't seem to cause any issues with advertising :)

That's because VAT is nationwide.

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.

What are the boundaries where VAT rates change? Within the US, there can be state + county + special tax district in the county + city + special tax district in the city.

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.

Plenty of things vary by location. Rent and wage have a bigger impact than sales tax on the final price in a supermarket. Yet they are able to coordinate sales prices even when the rent varies a lot, because anyway those are loss leaders and then the rest of items get the proper markup and differentiated prices depending on the location. Just like you have items in the RU with the same promotion prices in countries with 15% VAT and countries with 25% VAT, usually because you want the nice rounding at, say, 399.

That's not really true as a general rule. Grocery stores, for example, have an average profit of just 1–3%.

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.

That's the profit margin across all products. Consumers are not rational (or at the very least, not infinitely knowledgeable and able to use that knowledge instantaneously), so you would absolutely expect effects like charging 4.99 rather than some tax-adjusted number like 5.18 to translate into real profits.

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.

I don't, and will never understand this argument, because here in Europe, the Tesco in my town centre has a different price for the exact same item to the Tesco Superstore on the edge of town which also has a different price to the little Tesco Express down the road.

Somehow this all works magically here but in the US it is impossible because.. reasons unknown

So where you live there are no standardized prices by any chains at all for anything? No prices are ever advertised anywhere?

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 :)