Still reading the case in detail, but these quotes address your comments head on and indicate that SCOTUS likely would not support a state scheme allowing for a multitude of local sales taxes (a la California).
EDIT: While it is true that the dissenting opinions wanted Congress to solve this problem for them, the physical nexus rule was (and generally always has been) a construct of the Courts, and should have been struck down by the courts. Having a legislative counterpart is no excuse for letting bad decisions live.
EDIT2: Also, SCOTUS did not strike down the nexus requirement, only the specific physical nexus requirement of Quill. The dicta quoted below strongly suggests that complex sales tax system would require stronger nexus than the South Dakota regime.
"Complex state tax systems could have the effect of
discriminating against interstate commerce."
"That said, South Dakota’s tax system includes several features that appear designed to prevent discrimination against or undue burdens upon interstate commerce. First, the Act applies a safe harbor to those who transact only limited business in South Dakota. Second, the Act ensures that no obligation to remit the sales tax may be applied retroactively. S. B. 106, §5. Third, South Dakota is one of more than 20 States that have adopted the Streamlined Sales and Use Tax Agreement. This system standardizes taxes to reduce administrative and compliance costs: It requires a single, state level tax administration, uniform definitions of products and services, simplified tax rate structures, and other uniform rules."