In all fairness, the paper on which $100 bills are printed is quite worthless as well.

I think ever since people have stopped using gold and silver bullion (after arrowheads and knives) as currency items, there has been this consensus that money has the value that people give to it, not the value of its material (or, in BTC's case, immaterial) representations.

Further to your point: BTC at least has the property that someone cannot arbitrarily create a new unit (without doing the requisite, increasingly difficult, work).

What exists with BTC is 21 million or so unique valid hashes and no others can be created. With money, say USD, there exist trillions and no guarantee that some party (the government) will not create massive amounts of additional units.

What if, one day, someone equips with quantum computer + smart can figure out the private hashes in anyone's wallet base on the public BTC record?

Would the BTC become completely worthless immediately?

If it happened overnight - perhaps.

But the algorithms behind Bitcoin are agreed on literally by consensus, the clients in the network which reach a majority are in control.

If it became clear that something in Bitcoin was about to be broken, the algorithm could be changed to something more secure, if a majority agreed.

Past transactions would not be affected - they are immutable - and new ones would become safe.

It would also depend on the economics of said quantum computing. But yes, I'd expect the value to decline because one could not guarantee their currency anymore. Similarly if someone invented a teleporter that targeted US currency, it'd become worthless because a thief could just teleport it out of your pocket.

Not quite. USD will always be accepted by the United States Government. If you live in the US, you'll probably owe them taxes no matter what you're payed in, and as such, will always have some need for USD, and USD will always have some intrinsic value of "enough of this will keep the IRS from arresting me".

In the case of fiat money, it does have value because you have to pay taxes with it and anyone has to accept it for settling debts.

Isn't money made out of special counterfeit-proof paper? Making that paper valuable since you could use it to make money?

It's ability to be used to make better fake dollar bills would make it worth something, but the years in jail you might be subjected to if caught presumably drive the demand down.