Parkinson's schematic is ridiculously, well, schematic. And from this perspective in time, the usual ideologue's move of taking a concern of his time (anti-liberalism and big government) and claiming it applies over all time.
Democracies die because of too much welfare? Ridiculous! Is that how the Athenian democracy died, voting too much pay for jurors? Is that how Weimar Germany became Nazi Germany, because the burgomasters were drawing too much disability? Is that how the nascent Japanese Meiji democracy was snuffed into militarism with the Emperor's aid? Is that why Sun Yat-sen's democratic movement split into the Communist and the corrupt KMT, because they were voting themselves largesse? Venice's oligarchical democracy didn't seem to have any such problem before its conquest. And so on.
The monarchy to democracy progression is little better. I bet you could not name 6 clear examples of that, from the full sweep of human history. Certainly it doesn't apply to America, Japan, or Athens, which either went straight from aristocracy (such as it was) to democracy, or retained the aristocracy well into their democratic periods.
(I used to think my time reading people like Thucydides or Herodotus or Gibbons was wasted on trivia, but at least it saves me from grotesquely false simplifications.)
I often hear people speak of democracy as the next, or the final, inevitable stage of human social development. Its inevitability is usually justified not by describing power relations that result in democracy being a stable attractor, but in terms of morality - democracy is more "enlightened". I don't see any inevitability to it - China and the Soviet Union manage(d) to maintain large, technologically-advanced nations for a long time without it - but suppose, for the sake of argument, that democracy is the inevitable next stage of human progress.
The May 18 2012 issue of Science has an article on p. 844, "Ancestral hierarchy and conflict", by Christopher Boehm, which, among other things, describes the changes over time of equality among male hominids. If we add its timeline to recent human history, then here is the history of democracy over time in the evolutionary line leading to humans:
There are two points to observe in this data:
I do believe "progress" is a meaningful term. But there isn't some cosmic niceness built into the universe that makes everything improve monotonically along every dimension at once.