The supply and demand curves are not straight lines. There is not one unit price that consumers value a good at, that's why the marginal price that a consumer will pay depends on the quantity produced. The first most eager buyers would pay a higher price than the rest of the buyers you can find at higher quantities produced (but a lower price).
Tariffs eat into consumer surplus and producer surplus not just by raising prices, but also thereby reducing quantity. I think the only times you'd see no effect on consumer surplus via a tax are when the consumers are always going to pay a fixed amount regardless of quantity they can get (perhaps in some budget-constrained scenario), or if the amount of the thing that can be produced is fixed regardless of price; neither of these scenarios describes consumer goods.
Tariffs eat into consumer surplus and producer surplus not just by raising prices, but also thereby reducing quantity. I think the only times you'd see no effect on consumer surplus via a tax are when the consumers are always going to pay a fixed amount regardless of quantity they can get (perhaps in some budget-constrained scenario), or if the amount of the thing that can be produced is fixed regardless of price; neither of these scenarios describes consumer goods.