A Ponzi scheme fails when you run out of people to sell your Ponzi scheme to. It’s a directional linear flow of money. In the case of Bitcoin, however, the coins remain in circulation like a currency. Therefore, I reject the idea that “when all the coins have been mined bitcoin would crash”. Such a crash occurs when there is no scope for further growth, which would mean that there would be no reason to buy those coins and holding it would be useless because there would be no one willing to buy it at a higher price. This would result in a crash. However, in reality, Bitcoin would always remain in circulation and would serve as a stronger currency in comparison to other fiat currencies. So, people would want to buy it and stay 100% in it, so that they can retain their purchasing power and spend using this currency rather than any other fiat currency. Moreover, there will be cases, like machine to machine transaction, where spending using Bitcoin would be much more convenient. It would also be lucrative as a currency for trade because it would facilitate cost cutting. This demand for circulation would keep its price rising even after all of them have been mined.
A finer grained look into price fluctuation would depend on the marginal utility and time preference.
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