Constitutionally, states can't tax interstate commerce. That is a federal power.

A lot of states have created "use taxes" on goods purchased in another state and imported by the buyer. This is because requiring companies to withhold taxes for states in which they do not have a substantial business presence would be overly burdensome on interstate commerce. These use taxes are likely unconstitutional, but states ask their own residents to voluntarily report their cross-border sales, calculate their own tax amounts, and pay them anyway. I don't think the constitutionality has been tested from that direction, but it seems to rest upon an argument that use tax is valid, just because the goods were pulled across the border this time, rather than pushed, like all the other interstate commerce tax cases reviewed by SCotUS. As such, the only constitutionally valid use tax would be for goods purchased within your own state, for which the seller did not withhold and remit sales taxes. So cash-in-person flea market, swap meet, and classified-ad purchases, basically.

You only definitively have an obligation to pay tax on goods sold and consumed entirely within the same state. Traveling salesmen are insufficient to cause a company to qualify as having a substantial presence in a state--their sales are considered to be made in the state where their company is based, or in the state from which the actual goods were manufactured or shipped. I'd expect that e-commerce sites would be no different. If Amazon has an office, data center, or a fulfillment center in your state, you owe sales tax, and Amazon should collect it. If they do not, their site is just a traveling salesman, and your interstate purchase is subject only to federal taxes, rather than state taxes.

States bleat and squeal about loss of sales tax revenues to e-commerce sales by out-of-state companies, but they do not have a constitutional remedy for that, so too bad for them. Interstate commerce is explicitly federal jurisdiction. And Congress so far has not instituted any tariff/duty regime on goods crossing state borders. But it keeps coming up for votes, in Congress after Congress.

This isn't taxing interstate commerce. This is applying the applicable sales tax. There is always point of sale, in one state or the other. Some states choose to interpret that point of sale as being where the buyer is standing when making the purchase (ie the delivery address). Other states would say that it is wherever the server is (Nevada, ie gambling). A state demanding that online purchasers pay a sales tax is not taxing interstate commerce, it is enforcing a tax against sales occurring within its boarders. States do have that power.

The sales tax is not applicable on purchases that span multiple states. It doesn't matter how hard you argue that one state or the other should have the ability to tax a transaction, whenever there are multiple states in the equation, none of them are constitutionally able to do so. If there's an endpoint in one state, and an endpoint in another state, it crossed a border somewhere and earned the "interstate" adjective.

The state only has the power to tax intrastate commerce, where both buyer and seller are standing within its borders. If you are loud enough and persistent enough, you can even convince a seller to not withhold sales tax on a purchase where you are physically present, by making a solemnized claim that you intend to immediately export the goods you are buying out of the state. Businesses do this all the time. (But then they pay use tax for their own state, because it's cheaper and more certain than arguing their case all the way to SCotUS.)

The tax is an excise on the buyer. Sellers subject to the state's jurisdiction must collect it, by law, on behalf of the state, whenever they are able to do so. It is an undue burden on sellers to be forced to operate as tax-collection agents for all of the states, including those they have not directly chosen to do business in, by establishing some kind of persistent operation there. There are hundreds of individual jurisdictions able to levy sales taxes on the domiciled residents of their state making purchases within the borders of their jurisdiction. What a towering barrier to entry it would be if, in order to operate so much as a catalog mail-order lemonade stand, a business had to purchase software licenses or tax-handling services able to resolve taxes for all the states and territories, and all of their tax districts, and possibly also an alternate rate within that district.

Sure. I'd be curious to see some data on who actually follows through on this. Pushing the burden to the consumer to document these transactions doesn't make any sense to me. Additionally, I bet many consumers don't even realize when taxes haven't been paid during checkout.

It isn't anything new. When you order something from another jurisdiction you aren't a simple consumer. You are an importer, subject to all the rule of any other importer. Amazon just implements what everyone was supposed to be doing already.

Allow online sales to occur without sales tax and one day nobody will ever pay sales tax. Every transaction could be structured in terms of online order and local delivery. Starbucks could let you order coffee online, then pick it up at the counter. This is why states are moving on this issue now. Amazon is just the first to implement it on their side of the transaction.