That guarantee is sort of like the spark plug of the economy - because it exists (and because the US government was a thing) people initially believe in the value of a dollar (and the same thing happened with every currency) but the currency continues to have value (and has a value exceeding that initial US valuation) because other people will buy it as well.
Also, just for a moment, the statement: "Dollar has value, because even if no one will want dollar, government will buy it for dollar." - that's a fair bit of nonsense, outside of the dollar having an exchange value the dollar has no value - fiat currency (and even precious metals TBH) only have value to to the continued demand for them and if that demand falters or if people stop valuing a dollar at as many whoppers as it used to be valued - then bad things start to happen really fast and the government is pretty powerless to stop it once it starts.
Your argument sounds recursive. What does it mean to say the government will buy a dollar for a dollar? A dollar is only useful if it can be exchanged for things other than itself.
