Is it actually that common? Using a higher order function that returns member fields/methods which you then actually call?

Higher order functions are common in JavaScript, and closures are as well, but I don't recall seeing them used as substitutes for classes or vice versa for years at this point. With JavaScript you don't have to use closures and higher order functions to do modularization because you have classes, and you don't have to use the functor pattern (like Java before Java 8) because you have higher order functions.

ES5's syntax for object types looked a lot more like "closures with syntax sugar" than ES6 and later JavaScript syntax with explicit class declarations.