Before computers and databases, it was a valid excuse to say that merely calculating sales tax was burdensome for a retailer. Today, calculating and collecting sales tax is trivial--there are dozen of SaaS providers for online retailers, including Amazon itself.
As well, it wouldn't matter, because the price differences on most items would still be a lot more than the sales tax. No one would go online if the only difference was 6% or 8% sales tax. We are talking 20-30% differences in some cases.
What you may be talking about is the use (I call it property tax) tax that some states wish to levy on property that comes into the state and remains in the state. I agree, there would be no difference between items regardless of their origin in such a case.
However, fundamental to Quill was the burden that calculating a sales tax would impose on the retailer. In the times of Quill, incidental sales (in the case, less than a dozen over several years) to customers in North Dakota were not enough to justify the burden of imposing a sales tax; it would have cost Quill more to figure out the sales tax owed than Quill would make from the sale.
But technology has changed. The concerns raised in Quill are non-existent today; it is trivial and dirt cheap to calculate and collect a sales tax for all taxing jurisdictions in the U.S.
Amazon knows this; that is why it has always backed down when states threaten to pursue this issue in court (i.e., NY, Cali, and Texas). Indeed, Amazon now offers a sales tax calculation service to smaller etailers.
Note that most legal commentators agree that Quill could easily (and probably would) have gone the other way if the catalog company in the case had sold to more than a handful of customers in North Dakota.
1) Amazon, Newegg, etc come out and say "we love local businesses" - because honestly, who doesn't have their favorite local shops, knowledgable people who know you is great. They admit they have been hurting local businesses, and that they have an unfair advantage because of this show-rooming behaviour by consumers.
2) They roll out a "showroom affiliate" program. Businesses can sell the products, but they also can have a QR code or similar, with a "or get it on amazon!". This provides a commission to the store, recognizing that they played a part in the sale.
3) the show-rooming is not as harmful to the stores, the online retailer doesn't lose sales, and everyone can settle to a new balance.
This also gets the online retailers good press and warm glowies.