One huge benefit of (robust) type inference is type holes. That is the ability to leave parts of your code unwritten and have the compiler infer what the type of those unwritten parts should be, and in more advanced cases, fill in the gap with candidate code.

The latter is something that isn't in any languages I would consider production-ready (although it seems tantalizingly close), but the former is already quite useful depending on how much type inference your language is capable of. If paired with the ability to search for code by type, it makes exploring APIs extremely friendly. Even without that ability, I've found the ability for the compiler to tell me what type belongs in a given empty chunk of code to be extraordinarily helpful for those times that I'm programming in a top-down fashion (scaffolding first, then fill in the concrete implementation).