Type inference is not an exclusive feature of FP languages, though there is no known system that can deal well with nominal subtyping (scala makes a good go at it, but only locally).

What would you say is the usefulness and value of local inference vs global inference?

In my experience, local inference eliminates a lot of boilerplate and clutter, while global inference isn't so important, because writing types is good documentation as you zoom out from the details of functions.

It also emphasizes the importance of good tooling support: when using global inference it would be cool to always show the inferred types as a little semi-transparent text on the top...

Global type inference is the ultimate goal, local type inference is the compromise.

Global type inference would generate documentation automatically, to some extent.