Patents are not meant to be a way to stake a claim on an idea (https://www.legalzoom.com/articles/can-you-patent-an-idea) — they're a system where you get a temporary monopoly in exchange for sharing a novel, non-obvious and non-abstract invention.
To be clear, I didn't say that's what patents are for (i.e. their purpose), but what they correct for, i.e. what they do in practice.
But I don't see that the two descriptions are different in practice. Patents incentivize publicly releasing an invention instead of keeping it a trade secret (or letting it languish). The problem this is solving is that ideas aren't valued by the market, only products. But society benefits from ideas independent of products. And so the solution is a system to put value on ideas, ergo patents. This meshes with my alternate description.
