You need to go back to papers written by F.A Hayek criticizing Keynes in the 30s to get any serious academic discussion of the benefits of a fixed money supply. His critique of Keynes' idea of the "Paradox of Savings" is good, also the later paper he wrote: "The Denationalization of Money", which explores privately issued competing currencies is pretty interesting.
Note that a lot of Bitcoin enthusiasts plough through Keynes to the value of debt. This, on the other hand, was answered by the Battle of Waterloo, where the City of London financed British army beat the initially superior French.
"If it were possible, as has been repeatedly asserted in recent English literature,[114] to keep the total amount of bank deposits entirely stable, that would constitute the only means of getting rid of cyclical fluctuations. This seems to us purely utopian. It would necessitate the complete abolition of all bank money — i.e., notes and checks — and the reduction of the banks to the role of brokers, trading in savings. But even if we assume the fundamental possibility of this state of things, it remains very questionable whether many would wish to put it into effect if they were clear about its consequences. The stability of the economic system would be obtained at the price of curbing economic progress. The rate of interest would be constantly above the level maintained under the existing system (for, generally speaking, even in times of depression some extension of credit takes place).[115] The utilization of new inventions and the "realization of new combinations" would be made more difficult, and thus there would disappear a psychological incentive towards progress, whose importance cannot be judged on purely economic grounds. It is no exaggeration to say that not only would it be impossible to put such a scheme into practice in the present state of economic enlightenment of the public, but even its theoretical justification would be doubtful."
He's basically apologizing for finding all these flaws in the monetary system and central banking. He was convinced, at least at this point in his life that he could reason with the financial system to resolve these issues through better understanding. That's the interesting thing about Hayek. He was not opposed to the structure of the financial system out of ideological conviction but just that he had enormous insight into the dynamics of the system and stated his understanding without editing or simply repeating the conventional wisdom.
Economists have written on the mechanics of a Bitcoin-like currency, in essence, a fixed-supply alternative anonymous fiat "currency". The conclusion is that it will not be fulfilling its anarchist ideological aspirations by unseating the dollar. But it may have a place as an electronic equivalent of cash with appeal for illicit (read: extra-state) transactions.
My dismay with the Bitcoin discussion, as an economist, has been the level of confidence everyone comes with. Whether it is dismissing the last century of economics off-hand or arguing one position in a rich debate with dogmatic passion, it is difficult to have an informed conversation. This comes from both sides, e.g. deflation is good for a currency versus deflation causes a deflationary spiral, both highly contentious statements at best, comes up in every HN bitcoin discussion.