Yeah, US shops have to do that, in part as taxes vary from state to state (and sometimes community within a state) whereas MSRP are manufacturer specified. It's also legacy as there used to be price stickers which couldn't as readily be changed to match new tax laws for older inventory. Nowadays of course this has changed both with pricing guns and now electronic price signs.
There's also situations where untaxed items like clothing are taxed over certain values (luxury instead of poor necessity), which depending on discounts, may vary at the register.
It's similar to ordering something online or from a catalog, the shipping cost isn't known until after the items are cumulated instead of baked into the price. If those costs are included in the price the consumer typically ends up overpaying for that aspect.
(In recent times there's also tax amnesty days, like back to school clothing not being taxed for a week.)