Note that even Modern America has one office that is (partly) selected by lot: the office of Juror (of course in high-profile or otherwise significant cases, this random element has been almost entirely negated by sophisticated jury-selection methods employed by lawyers & prosecutors, with the aim of fixing the outcome in advance. But it still technically remains the official method by which jurors are selected).
We have modern computer systems and information databases (that people can’t escape even if they want to), so even though the pool of potential selectees is much larger, it would actually be easy to implement. Whether it would actually help would probably depend largely on the degree to which the staffers remained a permanent civil service.
I think people concentrate far too much on the importance of elected officials and their handful of appointees when it comes to the modern western beamtenstaat. (Plus, elected officials – up to and including the top level – come to office with almost no specialized knowledge. They come to office with, on average, a general law degree – which probably makes them worse, rather than better, legislators – knowledge of how to get elected, and knowledge of constituent service. They rely upon technocratic experts – in their staff, in the agencies, and in the outside interest groups they align with – for specialized knowledge. If there is enough public pressure on them and they think they’ll actually be expected to answer detailed questions about the legislation they favor they then sit on folding chairs in the basement of the capital to learn from their staffers what is in “their bills” – the ones they sponsor and ostensibly wrote. Maybe they’re good note-takers).
My personal guess is that election by lot might have made a difference if it was implemented before the “Civil Service Reforms,” but now it would make about as much impact as dropping a pebble into the sea.
The best quick, relatively short civics guide to modern western government is Foseti On Government Employment and This is Your Government. You can also take a look at The Three Branches of Government. an Austro-Libertarian might throw in The Federal Reserve as a “Fourth Branch,” but it’s technically part of the Bureaucratic Branch.
In order of importance, then, organizational reform would consist of:
1) Get rid of the Civil Service “reforms” – call it “updating for the digital age.” Go to a system where they can and will be broomed in toto (not just the handfull of “Plumb Book” appointees).
2) Did I mention “get rid of the permanent Civil Service?”
3) Repeal the 17th Amendment.
4) Election of Representatives by Lot. (Yes, Hoppe, yes – but at least there is a better chance that people selected by lot won’t be personally ambitious in the same way the self-selected political candidates are, and since it’s almost comically improbable that anyone would be randomly chosen to serve more than one term, they’d all know they’d be living under the laws they passed for the rest of us sooner rather than later).
But if you ever had the popular support necessary to implement any of those, much less all of them, you’d probably be at a stage where you could just implement something even closer to the Libertarian desire.