It doesn't follow that because you have frictionless transfer between two assets, the two assets do an equally good job of transferring purchasing power across time. All else being equal, you use the more liquid one for that. That's why the equilibrium is to converge on a single standard.
Why, and why not? We are not economists nor currency experts, so interested in the real reasons that this may be true.
Why liquidity is a desirable property of a store of value? It's the property that you can always find buyers or sellers at large volumes - what makes this thing useful to large players. It's also a necessary condition for having a deeply traded market - one whose price doesn't move much during large buys or sells.
That this property is very slow and difficult to achieve should be obvious. It's that chicken and egg problem that Bitcoin has been gradually solving, that's characterized by massive volatility. That volatility is a problem for those who are primarily interested in predictably transferring purchasing power across time, and its source is not yet having enough market liquidity (and in turn, market depth). If Bitcoin manages to achieve sufficient liquidity for large scale finance, then where's the incentive for the big players go through the slog of bringing another one up to speed, unless it offers some majorly useful technical breakthrough? And then wouldn't it be a whole lot easier, and financially less risky, to just upgrade Bitcoin?
Everybody acting like squirrels running from copycat to copycat is not conducive to very desirable stability, and so a Nash equilibrium is for large, thoughtful, entrenched interests to make up their minds and get on with business.
