The major reason given is that taxes vary so much in the US by location that it would be onerous for businesses with locations in different areas to print different price tags and advertise prices broadly.

It's even an issue online because, until you enter your address, the online retailer has no clue what your tax rate will be, and they have to assess tax based on the purchaser's location. Postal code isn't always enough, as they can be shared by different cities with different tax rates.

Some areas also vary tax by date (tax free holidays), though I don't think consumers would care if their total ended up being cheaper than they thought.

A national standard VAT would be the only way businesses might start including tax in price, but there's no way to do that without a constitutional amendment. States have the power to tax, and they're not going to stop now even if they receive VAT revenues.

So they did get you at 3.99 -> 3!

Maybe because your brain wanted 5+3+2=10 instead of 5+4+2=11 ?

How is that "weird"? That's just good numeracy.

Most people round down. Their brain locks on to the 1 of 19.99, and approximates it to 10.00. We need to actively counter this to see it as 20.00. It's a skill most people don't apply all the time, and a number can't even do.

Once you can do it reliably, it's mind-boggling that others can't, but it's still a learnt skill, that needs to be applied.

No, most people just give up after seeing the price.

No. Most people round to the nearest whole number and often just pick a direction to round.

Since no one does math in their head anymore the total is always more than they expected. No calculators on shopping carts anymore either.