Could eliminating all taxes and only creating new money theoretically work?
It would not work.
Historically speaking, governments that try to fund their operations primarily via the printing press experience not just inflation but hyper-inflation. Why? Well, one explanation is that without taxes nobody has any reason to want the government's currency. You can try to force people to use it, but that just encourages black marketeering.
Another way to look at it is that a policy of funding the government by printing money is equivalent to funding the government entirely with taxes on holding currency. But since the tax only applies to currency, and not gold, or land, or massive stockpiles of cigarettes, people have an incentive to avoid holding onto money at all costs. No matter the current price of cigarettes, using your spare cash to buy cigarettes for barter later on will always seem like a good deal because the cigarettes are more likely to maintain their value than the cash. But if no one wants cash, by law of supply and demand the value of cash should plummet.
Edit for the benefit of pedants: I am not saying that any &quot;inflation tax&quot; will automatically destroy the value of a currency. I am saying that people need reasons to hold your currency which are strong enough that they'll tolerate the inflation tax—and the larger the de facto tax on holding currency, the better people's reasons for doing so need to be. In the normal world, taxes are a key source of demand for fiat currency, take that away and the system stops working.