What does back bitcoin? It is more or less a game to consider that it is backed by demand.
Everything, by the same reasoning, is backed by demand. Houses, stocks, bonds, metals, food, guns, vehicles, goods etc., everything.
If new demand is "0" then the value of bitcoin may be "0" and it will be difficult to consider it as an investment or currency.
Again, that's true for everything. If there's no demand for a thing, it has no value.
If we imagine that all bitcoins are sold then new demand could appear only if bitcoin has been already treated as a currency
It's already treated as currency.
Today fiat is used to buy bitcoin on the market, then bitcoin circularizes in buy/sell process, then it come out to be changed for fiat.
Bitcoin isn't always exchanged for fiat. As said, it's a currency.