The issue with this point of view I have is that I think it's an oversimplification. Bitcoin is an awesome invention (maybe the greatest one of the young century until now) but it doesn't solve all problems of the world's economy, instead it could create new ones.
Hayek concluded from theory and a detailed investigation and analysis of history that free competition of currency can prevent the recurrence of severe inflation and deflation, which are still plaguing our world today. Free competition of currency can also deal with cyclical depressions and unemployment, deep-rooted diseases in the current world economic system.
Bitcoin, while it was created "out of thin air" at first, is essentially a deflationary currency, so it contradicts Hayek here a bit (if I understand that sentence correctly). The BTC money supply grows, but this growth becomes slower with every halving, and ends at 21 million.
Let's consider BTC becomes the dominant currency of the world. If the economic growth is stable or rising, the deflationary character means that prices measured in Bitcoin must gradually lower and lower. This deflationary tendency is already strongly visible, as we all know the long term Bitcoin price (e.g. the 1000-day average) has risen and risen, meaning that prices of typical goods and servicies in measured Bitcoin tend to decrease.
Now: is deflation bad? This is open to debate, there are people thinking that a deflationary economy would fit better with a world facing challenges like climate change, where resource usage should be lowered gradually.
But a shift to a deflationary economy would be a big change for the current economic "ruleset". For many publicly traded businesses it could become a disaster, because they benefit enormously from the inflationary paradigm. Fortunately there is at least a business type not affected too much from deflation: cooperatives, which are much more popular than many think, above all in Europe where in some countries they're among the biggest companies (e.g. in Switzerland and Spain). In a deflationary economy they could become a fundamental pillar.
But there is another problem. A deflationary currency could become
too attractive, meaning that there would be phases of extreme deflation when too many people buy and hoard (hodl) it. We've already seen that: 15% or even 20% or more of price increase in a single day has occurred several times in the Bitcoin world. In a Bitcoin-dominant world this would mean all prices would be lowered 15-20% in 24 hours, which is an almost safe path into instability. Such an extreme evolution can lead to a "bubblish" sentiment and in consequence to massive profit taking, making the currency "inflationary" again for a while.
This means while we fix one kind of "cyclical depression", we create a risk for another kind of "cycles": the crypto FOMO periods and crypto winters.
Fortunately there is perhaps also a solution for this, although it's a very unorthodox thought:
Bitcoin's money supply could be temporarily expanded if demand for it is too high. Obviously not in terms of "new Bitcoin added to the Bitcoin prptocol". But we've already seen such a mechanism:
bitcoin-based stablecoins, like BitBTC. These kind of coins could even be implemented perhaps on the Bitcoin blockchain itself, for example with a protocol like Omni or Counterparty.
In conclusion: I agree in general that Bitcoin can bring enormous advantages to humanity (and its economy). But that doesn't mean there are no challenges and problems it can bring, so we have to always think about (and try out) new solutions for these issues.