Not all states preclude including sales tax in advertised prices. According to this website,
https://www.taxjar.com/blog/retail/can-retailer-include-sale..., and by a quick count, at least 20 states permit combined pricing without any more limitation than a posted sign. That count excludes states which only permit it for a limited set of products and services, or which require sales tax to be itemized on the receipt.
Perhaps you're confusing VAT vs sales tax, which is an entirely different issue, and while some politicians might prefer a sales tax on the presumption of its conspicuousness, the real debate regarding adopting VAT is far more complex. VAT does seem to be the darling of many economists, but those economists also tend to overlook the fact that Europe has significantly larger grey and black markets, as well as more tax evasion, than the U.S.; and some of that difference is arguably a consequence of the mechanics of VAT and the general preference for hiding the taxation system from individuals.
It's also worth noting that there are good reasons for itemizing sales tax separately. For example, for individuals state sales tax can be deducted from federal income, but not the cost of the item itself.