I don't think it's just an assumption - I think it is fair to state that a currency whose primary mission is not to facilitate transactions will fail to catch on. So far BitCoin has failed to catch on.
Part of my original point was that currencies don't have "missions", people do. A person may or may not wish to own a bitcoin in order to facilitate transactions. A person might also wish to own one as a speculative investment. Neither "mission" is necessarily better than the other. Krugman just assumes otherwise.