Please do it Mr President. Imagine how high the tariffs have to be. Close to like 50-80% maybe? On all imports. That'll cut purchasing power so much.
And how effective will the tariff collection be compared to income tax? All the income tax workers will have to be transferred to customs. If the efficiency isn't similar, then US Dollar might have issues.
And it is much easier as of right now to evade customs and tarrifs than income taxes. You can undervalue very easily.
And with exports of China shrinking because of tariffs they'll be forced to increase domestic demand.
Yes, though other considerations such as practicality affect what's most efficient; a perfectly ideal system isn't the most efficient if there's no means or political will to implement it.
Why shouldn't it be? There are other ways to control inequality for a socialist state (since they control wages). All taxes (and rent, interest, profit) in a country are ultimately paid out on nation's labor. Taxing wages directly is the most sensible way of levying taxes as it doesn't have the risk of distorting the economy in unexpected/unwanted ways, and you can use progressive income taxes to readjust inequality.
Both the ussr and dprk control all/most firms in the economy. If they think that there is too much inequality in the existing wage structure, they can easily change it. As an example, the Chinese government implemented a salary limit on super high income earners in the state owned finance sector.