Steve Landsburg recently asked on his blog for anyone to offer plausible reasons for why cryptocurrency should have any value at all beyond just being in a speculative bubble. (Aside, you can tell how behind I am in my reading, etc. by the date of this reply.)
Here is what I left as a comment serving as my attempts.
Attempt #1: Suppose Steve decides he wants to retire and move to Paradise Island. He plans to liquidate his assets including current real estate to purchase a dream place on the beach. He is not alone as many are contemplating and acting toward just such a move. At the same time current real estate owners on Paradise Island are looking to cash in on the land run by selling existing places including raw land. Unfortunately, many scamsters abound looking to take advantage of a key information asymmetry--namely, that it is extremely difficult to determine who actually holds title to actual land. Fortunately, there is one source (a cryptocurrency ledger) that can validate with complete certainty which of these are legitimate sellers and therefore legitimate potential transactions giving Steve (and all others) good title to any purchase. [Note: While this is an extreme case, adjusting for real-world frictions and the availability of alternative solutions simply lowers rather than extinguishes the value of the ledger.]
Attempt #2: Octan Corporation is a multinational firm with extensive interests throughout the globe. As such it has continual needs to transfer liquid assets (call it money) between subsidiary accounts and with arms-length third-parties all of which can be domiciled in different states and nations with custody at various third-party firms. In the current/old world this is costly in a number of respects: It has limited availability since banking systems are open only at certain times and days of the week, it is slow since the clearing process is built on old architecture with a cumbersome and time-intensive trust/verification procedure, and it is explicitly expense in fees as a result of these prior two reasons as well as the regulatorily-driven limited competition for these services. In the world of cryptocurrency these costs are substantially reduced. Literally Octan can send $1,000,000,000 across the world at 11:59 PM on a Saturday completing the transaction in 10 minutes for <1/100th of current wire costs in fees.
Attempt #3: Steve has many opinions and predictions about the world. Unfortunately, talk is cheap. Many dispute his contentions with vigor. However, Steve is actually very often correct. To his frustration Steve's detractors seem to vanish once the reality plays out in Steve's favor. And even if they are around for Steve to claim victory, they usually move the goalposts rarely admitting defeat. This among so many other facts like lack of liquid collateral or basic counterparty risk means ex ante bets are rarely able to be made. Fortunately, cryptocurrency allows trustless contracts to be written between these parties creating vast potential markets and submarkets for predictions and hedging.
Attempt #4: Steve loves using his credit and debit cards. He is a "points guy" who has the obsessive hobby of finding and exploiting all the various opportunities including arbitrages that exist for non-cash transaction rewards programs (e.g., frequent flyer miles bonuses, cash-back rewards, etc.). Steve is like all consumers, though, in that he doesn't like transactions fees. Fortunately for Steve, many of these fees for him are being cross-subsidized by naïve customers who are not maximizing their points if using credit/debit cards at all. The fees are transactions costs representing the true costs of validating and facilitating financial transactions. These add up to hundreds of billions of dollars annually. Fortunately, cryptocurrency offers the potential to cut these costs dramatically by creating "trustless" alternative clearing options. It is trustless in that the two or more parties to the transaction do not have to know each other as the network ledger validates the funds going from A to B are both good and compete (irreversible). [Note: While today transactions on various crypto networks like Bitcoin seem painfully slow (minutes or longer), there are options of subnetworks that can reduce these to seconds. Also in anticipation of a common objection, the price volatility risk can be eliminated by adding entry/exit transactions for both parties on both ends of the crypto exchange (e.g., dollars for Bitcoin for customer A, Bitcoin transfer from A to B, Bitcoin for dollars (or other) for seller B.).]