That's rather innacurate, Sparta was never popular among clacissists, irregardles of the timeframe: Sparta has no literature, no philosophy, no drama, no historians, no nothing. How could clacisstists love the unsophisticated Spartans and hold them higher to the refined, well-versed, extremely sophisticated Athenians who invented philosophy, excelled in the fine arts, layed the foundations for the evolution of science, not to mention that they invented democracy - the actual democracy, not the travesty that bears its name nowadays.
So, no, the scholars throughout the ages, at least after the 15th century when they got freed from the boundaries of the medieval ignorance, looked back to the Athenians for inspiration.
But since they belonged exclusively to the elites of their times, that made them to overlook the most fundamental prerequisite for an actual democracy: the representation and active participation of all the free citizen in the common affairs. Their compromise - and that only after centuries of struggle by the "lower classes" - was to allow them a vote. And the active citizen of the 5th century Athens, became the sheepish voter of the 20th century western world.
And they call that democracy...