Accessing a paid service by taking the API key out of another app without the consent of the service provider would be theft of services. In most US states theft of services falls under the same law as theft of personal property.
I see. Would that also apply to e.g. circumventing a paywall to read an article?
Why not? You can't just someone else app and use it as if it was yours.
Sure you can, that is what this post is about, it's just not legal to do so. But just because something is against the law doesn't make it theft anymore then it makes it murder.