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Cosmere books have an interesting spin on it. First an important caveat: all powers require some sort of fuel in the cosmere universe, or some sort or store/release mechanism. Therefore while poor and rich alike can gain powers, being able to afford to use those powers can vary. Some individual series deets(all of these exist in the same galaxy, but across different planets and sometimes different levels of tech)

Mistborn starts out looking like it fits the comic, with main characters being halfbloods with noble parents. However, some of the supporting super-powered people don't have that background, and as you go down the series some things start revealing what people believe about the powers isn't quite true.

Stormlight doesn't follow the bloodline thing at all, and various people of all classes and bloodlines develop superpowers, and inheriting it isn't the mechanism at all. Money can be a limiting factor, but isn't strictly one.

Warbeaker is somewhat more mixed. There is a power system anyone in the whole population can use, but the logistics of using it means people in power have a much easier time getting the needed resources to use it at higher levels. The resource is kinda tricky, so it isn't something that can be regulated or even stolen, but can be gained by anyone who can convince, coerce, or pay someone for their resource(everyone is born with 1, but you need lots to be powerful).

In addition, of the 4 main protags, 2 are princesses of a minor tribelike country, one is mysterious and too much spoilers to discuss, while the 4th is treated as a minor God, but is treated that way due to a more unique power system, but also one that isn't class based. A bit complicated but a concept explained early in the book: Returned are people who come back to life, and people worship them because of two features they have: they might dream about the near future, but won't understand it themselves, and they can sacrifice their second life to perfectly heal any one person. They have limits I won't go into here though.

Summary: powers in their true form do not discriminate, but situations and societal structure allows some of them to be manipulated that way.