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Hallo Benjamin,
I am quite new here and also to the Austrian economics, but Saif got me interested som I am going through it.
From my point of view it would not make much sense for a government to buy all the Bitcoin with printed money as this will drive the price exorbitantly high (due to concentrated demand to buy it all as well as money devaluation due to printing) which would rather quickly draw the economy to hyperinflation and ending up with an asset that if they dont want to use it for anything will have zero value.
On the other hand you can convert your money obtained from bitcoin to other asset classes like gold or real estate and I thing that if this happened there will for sure the demand for some kind of hard money asset will create some viable alternatives.
And not to mention the fact that the gorvernment will need to buy all the newly mined bitcoin until 2140 for ever increasing price.
From this point of view it would be easier to seiz all or at least 51 percent of the mining assets.
Just my 2 cents, I might be wrong but this is simplified version of how I view it.
Thanks and take care