The two of my (American) kids who've gotten old enough to buy stuff on their own, even if it's just us sending them into a convenience store with money for something, have immediately recognized this system as idiotic, and they frequently complain about it. It's so plainly-stupid that, literally, even a child can see it.

Largely due to inertia, consumer psychology where lower sticker prices encourage more purchases even when consumers know the checkout price will be higher, and the fact that taxes can be different based on the type of item you are buying and the exact jurisdiction you are buying it. Two identical stores across the street from each other can have different tax rates if they are in different tax jurisdictions.

The stores have the info to calculate this, and do at checkout, so it's really the first two points mostly.

Because sales taxes are ussually set by the local jurisdiction.

So it could 10.25% in one place, 9.75% in the next town 8.750% and 8.975% if you drive for another 15-20 minutes. Imagine if you run a business, have multiple locations and want to buy a TV/Billboard/etc. ad with the price how would that work? You'd also need to make different price stickers, won't be able to print the price on the packaging etc.