The problem is people keep mixing up terms of republic and democracy. America (and extremely large portion of modern representative governments) is a republic. Oh more of a democratic-republic, to be sure, since we have some democratic elements, but I digress.
The question details flaws of what he describes as a "liberal democracy", one with different branches of government, with seperation of powers, etc...I would say the one and only flaw of said government would be the propensity of power to consolidate itself, and that is a flaw of all governments. The federal government, in trying to check and balance itself will become a bloated bureaucracy (such as was made fun of in Dave Adams' "Hitchhikers' Guide to the Galaxy"), and we've already seen that happen in many cases (think of how hard it is to get someone fired from a federal government job).
The problem with "minimalist democracy" as you label it, is it mirrors many "dictatorships" and "fascist" governments still around today. In pre-war Iraq, Saddam was often elected with 100% of the vote (if he was elected with 99% of the vote, his cronies probably butchered the traitor), and used that to show the world "his" people still loved him, then turned around and gassed, butchered, spied on, and mistreated the people of his own country. There is no "check and balance" to prevent that one person from consolidating power, which is the fundamental flaw of all governmental systems.
Power tends to Corrupt, Absolute Power corrupts Absolutely.