I know not a perfect example but that's my gist.
While I believe it is an interesting scenario. I do not envision something like that will happen. The only reason it might is for its "consumer protection" value.
I appreciate that Greg realises some of the promises of Bitcoin but the true value for "billions of people" is not an optimized "clearing house". I expect Bitcoin to scale to a point where the store of value and liquidity concerns are non-existent.
At this point, high-inflation economies will turn to Bitcoin, and not gateways that will convert their already worthless currencies to USD or whatever. This provided value will ultimately catch on over here at which point some will find it largely preferable to hold BTC and not their "normal currency. Hell, some already do.
That depends on what you mean by "large per-BTC price". It requires a certain minimum BTC price to move a certain amount of money when settling in bitcoin. You can't move $1M USD in one Bitcoin transaction if a single bitcoin is worth 1 cent and there are only 20 million of them. So the bitcoin price measured in a certain currency limits the maximum transaction volume for that currency when settling in bitcoin.
Secondly, and perhaps more importantly, it requires great liquidity/market depth. One must be able to buy or sell a lot of bitcoins without affecting the price. This is the essence of money: a high-liquidity commodity.
> I guess I mean "valuable" in the intrinsic sense, not the financial sense.
When settling in bitcoins, they need to have value in "the financial sense". That's a requirement.
If there are 20 million BTC in active circulation and the bitcoin network processes 20 billion USD per day in transactions, than the "intrinsic value" could be $7000/BTC if the average bitcoin is held for a week between transactions (eg, you are paid biweekly in BTC and spend them constantly), or it could be $40/BTC if the average bitcoin is held for an hour between transactions (eg, people hold fiat and the BTC are in constant use by the gateways).
A high intrinsic value really requires adoption both as a payment network and as a store of value.
This is a fundamental misunderstanding of Bitcoin. Because each and every Bitcoin function as a sort of "token" that provides access to this payment network, their value is closely tied to the value of the network. For Bitcoin to become an international payment gateway system, liquidity requires every Bitcoin to be worth a lot.