The reason sales taxes are not posted is at least in part because there can be several independent authorities that can and do change the sales tax on a whim. The sales tax you pay is the aggregate of these separate authorities. There is no central sales tax authority that keeps these changes on a sane and sensible cadence, which is one of the reasons sales tax is highly variable and hyper-local in the US.

In this scenario, it is much easier to change the sales tax at the register than to reprice the entire store every time one of the several sales tax authorities decides to change the rates or rules.