I used to share your confusion, so I asked some Americans and was partly converted. One reason is that having taxes "added on" means people are more aware of the tax rate and how it affects prices at the cash register.

Since there are sales taxes at multiple levels (another reason - taxes can change frequently and are far from national) having a feel for taxes comes in useful when voting since if you feel you're getting nothing for your local taxes, you can make an informed decision at the ballot box.