I disagree. When you start thinking about the size then you stop thinking about the purpose. And the purpose of components is to encapsulate functionality. If that functionality turns out to be a button that you can basically click and it will do something useful for you that’s a great candidate for a component.
That being said, there are 2 types of components that you will ever create: universal components that belong in a library and specific components which most likely belong to the application. The latter type will be created to serve a concrete purpose, like the button in the example.