Sales Tax is an indirect tax on consumption that is deferred until the end consumer makes a purchased, and taxed in the area they made the purchase (even online since 2018). Some end consumers are tax exempt and can avoid paying Sales Tax. Companies can write off taxes paid where appropriate. Everyone else in the value chain is tax exempt assuming they filed their paperwork correctly. Ultimately this means that there is no equivalent to a VAT recovery, reverse charing, etc, and the governments that collect sales tax don't see any money if something is never sold.
Sales tax is not included in the price because it is based on the price. If a widget is sold for $10 today, there is less tax paid if you sell that widget for $1 tomorrow. It doesn't matter if $9 of additional value was created along the way.
States, counties, and cities can have different sales tax rates for various reasons. For example, my city voted to add to the sales tax to pay for road improvements. There is a lot of travel into our area for consumption so it ends up that visitors pay for roads even if they don't refuel their cars in the city.
Sales Tax and VAT are not bad ideas, they're just different ideas. At the end of the day if your government wants a Dollar, a Pound, or a Euro, they'll find a way to raise it.