Call the "deadly contest" the way you want, the result were the same. And yes they were not the only ones. The Akkadians were rumored to do the same thing as were the Babylonians.
RUMOURED.
Come on. RUMOURED. It's all bloody rumours. Find an account from a society, written by that society, where they actually did the thing. Or better yet, find archaeological evidence. Funny how there never is any of either, eh?
Probably because it didn't actually happen! Maybe I'm wrong, but let's see some evidence, not trash-talk from some Athenian prat or whoever.
You say you're not ignorant, and maybe you aren't, but why then repeat dodgy rumours with substantiation or qualification? Like, let's look at Herodotus. The Father of History of the Father of Lies, depending on who you ask. Dude is either his direct experience (very valuable first-hand accounts) or metric tons of rumours. To him tell it, no-one ever took a city by siege, ever. There's always an exotic/romantic tale about how people snuck into a city, or there was a traitor, or whatever. I love Herodotus but he's full of nonsense. Half of what he's saying is probably totally true, and half of it is probably complete bollocks. And we don't know which without other evidence, and that's true of most "rumours".
The Spartans were a failed state from pretty much day 1.
They enslaved a much larger population (something rarely but not never seen in history before/since), and then had to refocus their entire society into violently oppressing that slave population (and no I don't agree that a better word is "serf", but that's a whole other discussion). Pretty much every decision they made comes back to "Oh crap there are so many of them, we gotta keep them from revolting!", whether it's their military machine (which was largely used to suppress said slave revolts), to allowing women to own property (which was necessary with the professional military taking the men away full-time), to the use of exposure (which was part of the propaganda machine that kept them fanatic).
And don't make me start talking about the 700 Thespians, either, who history loves to ignore. "300" my arse.
They managed to stop oppressing the slaves long enough to have one moment of glory, and history forever acts like they were amazing, when in fact they were idiots who happened to be useful in one particular situation.
As long as they could still do some chores to help the tribe they would be cared for.
I don't think there's any evidence to support that, that I'm aware of. Explanations like this fail to account for that fact that they're humans, and so very much bound by emotion and often irrational beliefs, rather than cold calculus. In reality there are going to have been situations where people who could do tasks were ditched because they were unpopular and/or the situation was desperate, and people who were almost entirely useless were kept because they were beloved and/or sacred.
There's a temptation, I think, to see the stone age/bronze age as a sort "post-apocalypse", but studies on actual H-G tribes tend to suggest it was more edenic than apocalyptic most of the time.