The current rate at which Bitcoin's purchasing power is increasing is obviously not sustainable indefinitely, but so what?  The "price" of a bitcoin doesn't need to increase exponentially forever in order to prevent some "scheme" from collapsing. Bitcoins are simply digital commodities whose value will continue to be determined by the intersection of supply and demand.  That value can go up, down, or sideways. And in fact, we've already had several extended bear markets where the price has fallen.  Now, your response might be something like: "Yeah, but the only reason people are interested in buying bitcoins is because they believe the price will continue to rise over the long-term and that can't continue indefinitely."  And my response would be to ask you to think about how money works.  No one actually wants dollars (or Bitcoins). They want stuff -- useful goods and services that can be used to directly satisfy their wants and needs. The only reason anyone ever agrees to accept money in exchange for providing something else of value is because they believe that later, they'll be able to exchange that money for something they really want. And note that it doesn't particularly matter whether people access the stored value represented by their bitcoins by exchanging those bitcoins directly for goods and services, or by going through the intermediate step of first exchanging them for fiat. (Consider that gold still serves a useful monetary function as a store of value even though almost no one "spends" gold directly.)

And so the inevitable end game for Bitcoin is not that you eventually run out of "greater fools" to sell them to; it's that Bitcoin's monetization reaches a saturation point. When that occurs, people who accept Bitcoin in exchange for fiat / providing goods and services won't do so because they expect its value to increase dramatically; they'll do so simply because they expect Bitcoin to hold its value (or increase relatively slowly at a rate that's commensurate with the growth of the underlying economy).