The problem of course is the payee can't verify that one of the owners did not double-spend the coin. A common solution is to introduce a trusted central authority, or mint, that checks every transaction for double spending. After each transaction, the coin must be returned to the mint to issue a new coin, and only coins issued directly from the mint are trusted not to be double-spent. The problem with this solution is that the fate of the entire money system depends on the company running the mint, with every transaction having to go through them, just like a bank.
The root problem with conventional currency is all the trust that's required to make it work. The central bank must be trusted not to debase the currency, but the history of fiat currencies is full of breaches of that trust.
A rational market price for something that is expected to increase in value will already reflect the present value of the expected future increases. In your head, you do a probability estimate balancing the odds that it keeps increasing.
The price of any commodity tends to gravitate toward the production cost. If the price is below cost, then production slows down. If the price is above cost, profit can be made by generating and selling more. At the same time, the increased production would increase the difficulty, pushing the cost of generating towards the price.
When someone tries to buy all the world's supply of a scarce asset, the more they buy the higher the price goes. At some point, it gets too expensive for them to buy any more. It's great for the people who owned it beforehand because they get to sell it to the corner at crazy high prices. As the price keeps going up and up, some people keep holding out for yet higher prices and refuse to sell.
As a thought experiment, imagine there was a base metal as scarce as gold but with the following properties:
- boring grey in colour
- not a good conductor of electricity
- not particularly strong, but not ductile or easily malleable either
- not useful for any practical or ornamental purpose
and one special, magical property:
- can be transported over a communications channel
If it somehow acquired any value at all for whatever reason, then anyone wanting to transfer wealth over a long distance could buy some, transmit it, and have the recipient sell it.
Maybe it could get an initial value circularly as you've suggested, by people foreseeing its potential usefulness for exchange. (I would definitely want some) Maybe collectors, any random reason could spark it.
I think the traditional qualifications for money were written with the assumption that there are so many competing objects in the world that are scarce, an object with the automatic bootstrap of intrinsic value will surely win out over those without intrinsic value. But if there were nothing in the world with intrinsic value that could be used as money, only scarce but no intrinsic value, I think people would still take up something.
(I'm using the word scarce here to only mean limited potential supply)