A couple of points, though:
-Sparta of that time period was extremely small by today's national standards, but still larger than a few thousand. Scholars generally estimate the number of Spartan citizens to be around 30,000-50,000. Helots (who were basically slaves, descending from non-Dorian peoples that the Dorian Spartans had conquered) probably were some multiple of this, maybe 4-5x. The perioikoi, or neighboring "allies", probably numbered around 50,000.
Still, your overall point is clearly right; the Spartan citizenry could have comfortably fit into a small baseball park. But, of course, this was true of almost all the other Greek states.
-With regard to punishment, I think it's problematic to use the example of Xenophon's Ten Thousand as representative of Greek practice in general, let alone Sparta in particular. The Ten Thousand of the Anabasis were a "multi-national" (deriving from many Greek poleis) mercenary army hired by an aspirant to the Persian throne. Like all mercenary forces, the principles of leadership and discipline were somewhat different from national forces. The leaders were elected by the troops, and the soldiers saw themselves much more as an assembly of peers than a strict hierarchy. I believe this explains the incident that you cite.
My impression is that even within the armies of the various Greek states, methods of discipline may have varied widely, reflecting the equally wide differences in the character of their respective societies. In democratic Athens, where the generals were elected in political elections by the citizen-soldiers themselves, the way that they were disciplined, particularly for more "day-to-day" offenses, may understandably have been different than in authoritarian Sparta, where kingship (which basically meant generalship) was hereditary.
That said, I suspect that it's generally correct that, for the most serious offenses, punishment to honor and civic participation was considered as vastly more important by most Greeks, wherever they lived, compared to modern times. I think this is due to 1) their shared cultural touchstones (the Iliad and Odyssey essentially had a status for all the Greeks that is similar to the Bible/Koran/Torah today, that is to say, as a primer for values), and 2) it's hard for modern people to fully appreciate, but for the Greeks, one's polis was one's world. As a general rule, one was born into membership of a small, intimate club. One couldn't simply pick up and attain citizenship status in another Greek city-state if life was made unbearable in your own (although it was possible to live as a kind of resident alien). And moving to live permanently with "barbarians" was out of the question for most Greeks. Hence the effectiveness of the disciplinary methods you mentioned.