I don't think any society ever organized the way Starship Troopers works.
I know a few societies offered foreigners citizenship after they served, but, like the Roman empire, these were dictatorships where voting was either irrelevant or simply didn't happen.
However, "skin in the game" is usually taken to mean "owns property" and many, many societies have required a person to own property before they could vote. Including ours.

There's a logic to this, because in a primitive sense, the reason we vote is to avoid civil wars. And it is the property owners who would be supplying the munitions, victuals, and uniforms to the armies that might fight a civil War or revolution. At the time of the first French revolution, France, the US, and England all only let people who owned property vote. All three countries found out, in different ways, that even people with little or no property can make life very difficult for everyone else if they feel oppressed.

The other lesson to learn from looking at the three histories is, even if the desired endpoint (universal manhood suffrage) is obvious, you can't just rush into it. France tried to go from only about 1 in 100 men being allowed to vote in 1789 to letting all men vote in 1792. It was a disaster, and it quickly became a dictatorship. Then they repeated their mistake in 1848 and once again a mass of inexperienced voters inadvertently got themselves a dictator. The US and UK got to universal manhood suffrage slowly and incrementally. In France, the politicians were open about their end goals and things moved fast. In the US in the uk, the politicians were always cagey, and even hypocritical. "Oh no I don't want all the bipeds of the forest voting, I just want to expand the franchise a little bit!"

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