Why do so many businesses share their data openly, for free? Most often, the answer is scale. As companies grow, the staff within those companies realize they have more ideas than they have the time and resources to develop them. It’s typically easier to work with other external companies that specialize in these ideas than build them in-house. By creating APIs, a company allows third-party developers to build applications that improve adoption and usage of its platform. That way, a business can build an ecosystem that becomes dependent on the data from their API, which often leads to additional revenue opportunities.

it seems like a perversion of my beautiful REST/JSON server

My UIs are data/store driven. The UI is just a way to visualize the data. Your data could flow through all of of the extensions and the extensions can make decisions (e.g. setting visible to false). Like middlewares in a Connect/Express/Polka app. And the UI doesn't even know about all this, it just updates with the current state and makes sure it's consistent.

This is done to separate internal representations of information from the ways information is presented to and accepted from the user.

React is an isomorphic/universal framework. That means that there is a virtual representation of the UI component tree, and that is separate from the actual rendering that it outputs in the browser.

As a result, web browsers can provide only minimal assistance to humans in parsing and processing web pages: browsers only see presentation information.