Dear John Werner
The US Constitution has no such provision. Please recall that Article I., Section 8. states that Congress has power "To regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes" (one of numerous powers enumerated there). Perhaps you were thinking of Article I., Section 9., which reads "No Tax or Duty shall be laid on Articles exported from any State" (one of several limitations listed there)? Note that Article I., Section 9. contains only limitations on federal powers (in this case, a limit on the power of Congress to regulate interstate commerce); the limitations on state powers are found in Article I., Section 10. (For example, the power to grant titles of nobility is forbidden in both Section 9. and Section 10.; the former forbids the federal government from doing so, the latter forbids state governments from doing so.) Because state powers aren't limited in Section 9., and no corresponding article to limit the power of states to tax is found in Section 10. (although a limit on the power of states to lay duties on exports is found there), states are able to lay taxes within their respective jurisdictions (such as sales taxes or use taxes) on articles exported from any state.
Ed Gould, one of the reasons why sellers might care is overhead: they would have to track and remit the collected sales taxes to the relevant state revenue departments on a regular basis, and they would have to keep track of modifications in sales tax legislation, both permanent and temporary changes, for the forty-some-odd states that have sales taxes. (As Mitch alluded to above, the goods and services that are subject to sales tax vary by jurisdiction, and a jurisdiction as small as a single town can have a distinct tax rate from its county, and the county can be distinct from the state, &c.).
Simpson, that's the crux: is the New York presence of Newegg a physical presence? If not, then there is no need for them to have a registered agent there, and the scenario would be moot.