Money/labour input does not equal value. I could spend 10 years pulling all the grass from my backyard and sorting it from longest to shortest in length. A lot of effort went into it. Doesn't make it valuable.

Paper money is backed by the willingness of other people to price their goods and services in it. If people stop pricing their goods and services in it then it is no longer money. eg: a Zimbabwe dollar is no longer money. No one will exchange anything for it except for a novelty value.

Generally vendors exchange those paper monies for goods and services due to the requirement to pay taxes in fiat dollars. Vendors aren't required to sell for dollars, they can sell for whatever medium of exchange they want. It's just convenient to do so due to the tax reason. That reason alone can't save a currency though. eg: $Zim.