I'm not the OP, but here's how my Rails app is growing after several years:
The first "complex" UI design that we came up with was creating a list view that came with all the trinkets you'd want from a sophisticated list view (pagination, sorting, filters, searching). This view needed to be able to apply easily to all the key data structures our app uses (list of users, list of things user has, list of things users do, etc) which meant due to the scale of some of the data sets most of the operation work needed to be on the backend.
Originally, it was built as a completely normal Rails view requiring a full page refresh (form submit) to perform any given operation. This certainly was "doable" but not a great experience as someone administrating lists of things in our app.
We then wrote a React component that manages all the visual state itself based on the data returned from the backend and replaced the existing Rails view with this React component. By pushing responsibility of view state to the client our Rails codebase get simplified. React fully manages visual state, but where we really benefit is the fact that it forces you to design components in such a simple way that UI abstractions become more naturally fitting. The conventions are easy to understand and result in a codebase that can have a lot of cooks in the kitchen without too many problems.
Could this be written in jQuery? Sure. If it's like most large jQuery projects I've seen with multiple hands on it, it will be hard to keep it from being too brittle.
The implementation is really part of a longer term plan to begin building out new user interfaces in React. We find that react delivers on the promise of UI reusability much better than any backend MVC frameworks view or partial system. A front-end codebase is starting to emerge with it's own developer conventions and processes that are more geared towards frontend requirements. Meanwhile, our backend is simplified to only deal with tasks related directly to data management. The split feels very natural as the codebase grows larger. There is no obvious downside to writing in React besides the minified library code payload.
As a summary: our users expect interactions with complex interfaces to respond quickly. React is designed to build interfaces that fulfill that expectation, and the implementation of React in our codebase allows to slide into a more microservices looking architecture in an organic way as the scale and complexity of our app increases.