Money, medium of exchange vs store of value?

By intrinsic value I mean this: assume the object was declared illegal to be used as payments of any kind. Would people want that object for some other purpose, enough to pay something for it? If no, that is what I mean by not having intrinsic value. Where I live, leaves are piled up in the street, free for anyone to take, but nobody does. Certainly no one will pay for them. So that where I live, leaves have no intrinsic value. Dollar bills, if declared illegal to use as money, would probably be dumped in the streets, too. So they too, have no intrinsic value.

Now it may happen that dollars will be worth money to someone, as wallpaper or novelty toilet paper, or to wrap fish, whatever. Maybe they will sell for ten cents for a pound of paper money, whatever the denomination. In that case, the intrinsic value is so much less than its current purchasing power that I would also say, though not with 100 per cent accuracy, that it has no intrinsic value.

As far as bitcoin, it seems to be based on something that has intrinsic value, idle computer time. One lets the network use ones computer and in return gets a bitcoin. So that the bitcoin is more a record keeping device, to keep track of how much time you have already given, and are therfore due something in return.

If a group of people would voluntarily get together and decide to use money that no intrinsic value, well that would be an interesting experiment. My guess is that the money would fall by the wayside.