Frankly, I'm amazed that Americans put up with the idea of picking up an item with a price on it, and then being charged a different price - but I suppose the heavy social bias towards tipping (rather than increased wages) means that tends to happen in other scenarios anyway. It would be completely viable to quote prices including tax in the US, companies would just have to deal with a variable profit margin rather than consumers dealing with a variable cost, but I think the motivation not to move to such a scheme is the 9.99 effect: people will tend to buy things which seem to be better value without putting more than a trivial amount of thought into whether the thing actually is better value.
Keep in mind, we have no national consumption tax. Some states have none. In other localities, with state, county and city taxes combined, it can exceed 10%. Considering the hundreds if not thousands of possible permutations, it would be confusing if not impossible for online retailers (in particular) to advertise the exact price to every customer. The system is "different," if only because the US system of government is far more decentralized than most nations, but you get used to it.
The real problem with the system is that it's porous beyond belief. Ordering goods from out-of-state retailers to avoid paying sales tax is a routine tax dodge in the US. The states are trying to crack down on that method of avoidance, but it's expensive for the states and frustrating to tax payers, since (in California at least) they are using business income tax returns to trigger audits. We got gaffed that way this year.