The government collects taxes denominated in USD which is enforced with violence. This is why USD is in demand. As soon as this (in case of income tax even unconstitutional) collection mechanism by force fails the dollar becomes worthless over night.
You really need to look into the history of currency of you truly believe any of this.
Currency is worth something because other people are willing to trade it for something useful at a stable exchange rate. Now, having a central bank that controls the currency, and a government that enforces that control, can help protect the stability that gives that currency value in times of economic instability, but that's only occasional interference.
We know this because, in the past when states were weaker and less able to do this, huge swaths of people ignored their state currency, more or less, and used other states' currencies, ones that were more trustworthy (counterfeiting used to be a serious concern) and stable.
Even today there are countries where people are in practice using the US dollar as their currency, ignoring local official currencies, simply because the dollar is recognizable and its price is extremely stable compared to their official legal tender. How does this square with your theory that the dollar would lose all value overnight if the US government stopped requiring it?
