Do people commonly think types are a solution to most or all problems? Other than correctness I am not sure what software engineering problems a type system actually solves, and the rest of the debate is about the expressiveness of the type system (or lack thereof, which forces suboptimal engineering practices in some languages).
Static typing is just another form of static analysis. However, it's static analysis enforced by the language rather than a third party tool. That allows me to be confident in my dependencies too if I see them putting the type system to work.
Protobuf is moving us that way with microservices too. Since they're a strongly typed message format, it's harder to make mistakes in the interface between two services.
I also like that languages can have complete local static analysis. Sure, the business requirements might be large and spread across many areas, but I will break them down into smaller chunks and encode invariants into the type system so that if the small chunk compiles, I am confident it does exactly what I expect, and I don't need to remember exactly where it fits in the larger picture
