You cannot regulate what you have banned. Furthermore, do you see any definition in the US Constitution which defines as a crime, trading with anyone?
This isn't about implications. It's about simple facts. The purpose for regulating commerce with foreign nations was simply so that no state could end up with an advantage over another state when drawing up trade agreements. It was NOT to eliminate trade with any particular nation.
I've explained this to Poobah but the government doesn't posess any power that it cannot derive by your consent. You first must posess the power for the government to use it. You nor I have the power to prevent anyone from trading with anyone else. Thus we cannot consent to anyone to use such a power.
If the government is using a power that you didn't first posess, then it is operating by force and fraud.
Since the Constitution invests the Congress (elected by the consent of the governed) with the power to regulate trade with foreign nations, the Constitution leaves it to Congress to define the particular crimes. Treason is the only defined crime in the Constitution, but that doesn't prevent Congress or the state from passing laws which define other crimes and set consequences for committing such crimes.