"I have programmed in Servlets, JSP Model 2, ASP.NET, iOS, Android, Windows". I suspect in those kind of applications your state management library is just your database. In lack of a database and having the need of reacting on data changes, single-page applications typically resort to some kind of state management library.

In fact, with the Meteor framework state management largely revolves around a client-side reactive mongo API on top of your data, which IMO gives me the best developer experience.