Playing devil's advocate, for a moment (2nd time today, I just notice)
Not challenging the 'minimum valuation required to perform as medium of exchange' argument. But why can't the ledger be separated from the currency function? For a number of imaginable functions in the future, a minimal share of the supply would be enough to perform the ledger function (e.g. contracts).
In order not to gloss over this: there's still the valuation through required security. If contracts on blockchain have a certain total value, the network needs to be at least protected to make an attack economically unfeasible. Since miners are economically motivated as well, this will provide a security-based minimum valuation of Bitcoin in the process.
Still, the two values need not be the same, so the question remains: why can't the 'ledger' function not be separated from the 'currency/money' function?
You could separate the currency from the ledger, but to what end? Seems to me like that would be making the system and incentives needlessly complicated and would still require you to purchase tokens in order to pay your way into the ledger. In some ways, that is exactly what Ethereum has done. Either way the tokens are still required to make the ledger function, so why make them separate? Perhaps someone has an idea as to why this would be desirable?
My mistake... could have phrased that more clearly, I guess:
I don't suggest we "split up" Bitcoin. My question was, "what prevents the rest of the world from adopting Bitcoin, the distributed ledger, but (mostly) ignoring Bitcoin, the currency"?
The usual argument goes "the two functions cannot be separated, so the above is impossible". I'm asking, why? To me it looks like a possibility, and the implications for total valuation in the long term would be drastic.
I suppose that is possible if we were primarily using the Bitcoin blockchain for contracts and properties, a la colored-coins or Mastercoin. But it seems to me that the primary use of Bitcoins will still be as an object of value in and of itself, used for the purpose of wealth storage and transfer. If you wanted to use the blockchain as a contract or property ledger only, you would then have to transact the value portion of that contract outside of the Bitcoin system, which then removes the real advantages of using Bitcoin in the first place.