There have been many fiat currencies in history to look at. It doesn't take long to see that pure fiat currencies really are based on the full faith and credit of the issuing authority. These issuing authorities don't have to be governments; the only thing stopping private parties from issuing currencies is just that governments tend to see that as muscling in on their turf, but it's not otherwise impossible or even particularly difficult. (Getting everyone to accept your currency is what is difficult.) The US dollar is a derivative of the US government. Something that is not a derivative of the US government is something other than a "US Dollar". The US government really couldn't start a new currency because the base case of the currency, what it really is under layers and layers of finances and financial structures and loans and everything else, is "what the US government accepts".
Again, the hypothetical is impossible anyhow, which kind of skews how you think about it, but at its core, at the deepest level, what the US Dollar is is what the US government accepts as payment, and below that, the fact that it is the US Government that will come after you if they are not satisfied with your payment. Anything else that they would accept for the same reason is basically the same thing as a US dollar as a result, and if the US government tried to create "multiple currencies", the financial system would swiftly come to an exchange rate based on precisely how much of the US Government threat can be avoided with each one. That is the base case upon which all the further recursion is based.
And again, I'm not making any more claims beyond "that is what it is"; I'm not saying that's obviously good, or that's obviously stable, or that anyone who questions it is an idiot... this post is simply about understanding what is. How you feel about what is, and what further conclusions you come to about what is, are up to you.
This is where I disagree with the maximalists of specific cryptocurrencies. If utility means anything, better payment networks will emerge as tech advances.
Of course gold solves for both of these issues.
Agree with your other points to a degree. Cryptocurrency is derivative in that it discounts the heavily regulated financial markets. The easy money policies can be viewed as part of that. Part of the value proposition in users choosing voluntary means rather than collaborating with coercive money.
Even for a simple use case like online shopping there is regulatory overhead. Chargebacks, merchant agreements and AML considerations all come into play. Try billing users $1 or 25 cents with PayPal as an example. Most shops won't allow you to buy a pack of chewing gum with a card.
It is a crucial difference.
If you want to say, this isn't really that solid a foundation to build a money system on... hey, I'm right there myself, honestly. The US dollar really is based on "the full faith and credit of the US government", and specifically its ability to project power in order to harass people failing to pay its taxes. Looking out into the world, I'm seeing a negative first derivative on that, and possibly a negative second derivative too. But that is still a cut above the nothing standing behind cryptocurrency. At the present time, based on its behavior, cryptocurrency is a derivative of the US dollar and is dependent on it and the prior low interest rates it had, not a separate entity with its own trust base.