Why should Bitcoin have a monopoly? If Satoshi2 comes up with another process, similar but differing only in the mining computation, my Bitcoin2's should be equal in value, or at least at guaranteed at an exchange rate based on compute intensity required.
I assert that they would not be my Bitcoin2's would be worth less. This highlights the observation that literally all of bitcoins value comes from confidence that the network of willing participants is permanent and robust. This makes it different than gold -- gold is gold, whereas one crypto-currency is entirely different than another crypto-currency. This also makes it different than other fiat currencies whose network of participants is compelled by law.
We can't have a currency competing with the US dollar. If I was the US, I'd love a domestic (crypto) digital dollar. If bitcoin fails people lose faith, and I present the solution for a modern society: the Digital Dollar, unbreakable crypto and easy for world-wide use and backed by the full faith of the US government/NSA. And: I could tax every transaction, even the smallest ones on Craigs List/eBay.
Gold is also a bet, just like Bitcoin, that it's the most marketable commodity (more than 90% of value is in this speculation, not in production demand). People tend to come up with valuing most the money which is most liquid, most accepted by others. If Bitcoin2 comes along it should be so incompatible with Bitcoin1 and so much superior that people would want to make that bet again with Bitcoin2. Most probably, though, Bitcoin1 would be extended since it's possible and so many people desire these new features. If not enough people desire new features, then another currency wouldn't be as liquid as the first one.
I assert that they would not be my Bitcoin2's would be worth less. This highlights the observation that literally all of bitcoins value comes from confidence that the network of willing participants is permanent and robust. This makes it different than gold -- gold is gold, whereas one crypto-currency is entirely different than another crypto-currency. This also makes it different than other fiat currencies whose network of participants is compelled by law.