Actually it does make sense and is done even today.
Banks, physicians, laywers and many other trades must be state approved to operate within the state and, even if I have the approval of a different state, that (alone) does not allow me to engange in trade in the other state!
The states have always had the soveriegn right to dictate commerce laws within the state - but if they DO allow other businesses from other states to engage in commerce in the state; all actors must be treated as equals - that is what the regulation of interstate commerce is all about. Indeed, without the clause, there would be anarchy in interstate trade.
This is further evidenced by the jurisdiction clauses for the Supreme Court “... to Controversies between two or more States; between a State and Citizens of another State; between Citizens of different States ...” as most “Controversies” are of contractual or trade nature and, if the federal government did NOT have the power to regulate, the court could have no jurisdiction!
The important thing to remember is that the states are sovereigns and the “United States” was a compact of the several states to protect and foster thier mutual interests.
Can a state disallow interstate commerce, but allow intrastate commerce even though the out of state businesses meet all the same requirements as the local businesses, except for being out of state? IOW, could a state simply deny it's markets to businesses in other states in order to create a captive market for it's own industries?