No, of course not. React proposes to replace one "best practice" by a different one. In React, the best practice is to divide your application up in a deep hierarchy of components, each of which adds one single little layer of abstraction over the other. Then, put all the logic and presentation that's relevant for that little piece of abstraction together inside that little component.
This way, you have very good separation of concerns - all "Button" stuff is together in the Button component, all AreYouSureDialog stuff is together in the AreYouSureDialog component (which in turn uses Button components), and so on. Because components can only interact with each other via props and refs, you also have very fine-grained control over the interface: it's difficult for the programmer of a parent component to influence the behavior of the child component any further than by the interfaces that the child component explicitly exposes for that (= props, and public methods for use via refs).
How is all that a "get out of jail free card"?
I've found that this design principle works very well with teams, even with junior team members. I've seen people who had never gotten further than building 10000-line CSS files with all kinds of horrible hacks let loose in a React project. After we explained the component principle and made an example component to easily copy&paste, they independently and without further encouragement started making React components for each little possibly-reusable part of the application. Buttons, frames, dialogs, cards, lists, you name it. React really makes it easy to make well-structured code and difficult to make things a mess.
I don't see how and of this impacts any of the responsibilities you mention (good UX, accessibility, etc) so I can't respond to that part of your comment.