The US has too many tax permutations for this to be practicable. Companies would have to make prices a bit higher to accommodate unexpected sales tax increases in some or other jurisdiction.
There's a small industry that specializes in knowing what the sales tax for a particular transaction should be at the moment it goes through.
That would centralize power to the larger taxing authority.
Right now, there's a huge number of elected people in the US who wield real local power through these taxes and other rules that they can make.
It's a headache but we live in the computer age and we can automate administrative things like tax calculation at checkout; we should be using systems to aid decentralization and democratization instead of the opposite.