In EU internet purchases were always taxed, and yet online-only competitors still manage to compete with brick-and-mortar stores very successfully. So this article is quite bollocks.
Over the pond it's the same for everybody. Doesn't seem so in the US.
But what can't happen is a situation where Herning, Ishøj, and Copenhagen charge different rates for different products. That simplifies the system considerably.
Correct me if I'm wrong, but an import duty was not part of the sales tax bill.