I'm curious how much of the perceived benefit of republic-based democracy is based in logical fallacies and myth.

Voters are irrational and on a long-term scale, growth in state power eventually leads to the circumvention of public involvement, counter to the very definition of a republic: "A republic is a form of government in which affairs of state are a 'public matter', not the private concern of the rulers".

Constitutions were the obvious solution to this problem but they are very rarely considered absolute law in modern times, which almost defeats their purpose. Their influence worn down over decades of tinkering and executive-branch expansions in power.

Constitutions were not the solution to the problem. An educated and engaged electorate was the solution. The Constitution was a framework for that electorate to use as a tool, but several of the founders were very clear that the essential requirement of effective government was the engaged and educated electorate.

James Madison:

  * The advancement and diffusion of knowledge is the 
    only guardian of true liberty.
  * Knowledge will forever govern ignorance, and a people 
    who mean to be their own governors, must arm 
    themselves with the power knowledge gives.
  * Learned institutions ought to be favorite objects with 
    every free people. They throw that light over the 
    public mind which is the best security against crafty 
    and dangerous encroachments on the public liberty.

Thomas Jefferson:

  * Every government degenerates when trusted to the 
    rulers of the people alone. The people themselves, 
    therefore, are its only safe depositories. And to 
    render them safe, their minds must be improved to a 
    certain degree.
  * Above all things I hope the education of the common 
    people will be attended to ; convinced that on their 
    good sense we may rely with the most security for the 
    preservation of a due degree of liberty.
  * I know no safe depository of the ultimate powers of 
    the society, but the people themselves: and if we 
    think them not enlightened enough to exercise their 
    controul with a wholsome discretion, the remedy is, 
    not to take it from them, but to inform their 
    discretion by education. this is the true corrective 
    of abuses of constitutional power.