If the value of a dollar doesn't depend on supply, we could print infinite amounts of it and reach infinite wealth. This false notion has caused so much misery in the last couple of centuries. Unfortunately value of money is also subject to supply.

>The value of money depends on the underlying asset

Printing more dollars does not create more 'underlying assets.' Therefore it doesn't make sense to claim there will be no effect on value of money if more money is chasing the underlying assets. It's quite possible the value of the dollar decreases.

Using your own definition, which itself is debatable, it is guaranteed the value of money will decrease if you only change the supply of money and nothing else.

Fiat money is absolutely printed out of thin air and it isn't backed by any asset. It is backed by the stability of the government that issues it. There is no amount of gold that can back a monetary system to sustain the levels of spending that we're seeing the US and other governments do, which is why most if not all modern governments are no longer on the gold standard.