The thing that sold me on React was this statement: "Most people make the mistake that the DOM is a place you put things."
The DOM is what the user sees. That's all. With React, you have a virtual DOM that can hold everything, not just what the user sees. It's a pure data structure, and can be manipulated as such.
Because that DOM is a pure data structure, React can figure out for you what parts have changed, and re-render those bits as needed.
I agree with you that React's virtual DOM is a real breakthrough. However, that doesn't make all of React worthwhile. Other frameworks can (and should) integrate a virtual DOM.
The DOM is what the user sees. That's all. With React, you have a virtual DOM that can hold everything, not just what the user sees. It's a pure data structure, and can be manipulated as such.
Because that DOM is a pure data structure, React can figure out for you what parts have changed, and re-render those bits as needed.