Static types can absolutely help with more than local reasoning. One of the main reasons I like static types is that they give me a place in the code to reflect aspects of the architecture that otherwise go implicit. Databases are a great example: in both static and dynamic languages, the behavior of your code is going to depend on the database schemas you're using, and static types give you a mechanism to declare and manage this dependency explicitly. In a general sense, the key in architecture is how a system is split up into parts and what interfaces the parts have, and a static type system is a way to make those interfaces first-class citizens of a language subject to abstraction and automation.

Code with static types might be larger than the problem it's trying to solve, but so might code with dynamic types—that's more a function of the sort of abstractions and complexity that go into the code. I've written some code to do very similar things in Haskell and Python, and my experience is that the Haskell code tends to be noticeably more compact than the Python code, even though I make liberal use of types and write out all the top-level type signatures. While some of this comes down to other differences between the languages, part of Haskell's expressiveness absolutely comes down to static types—static types make it easier to write very general code against high-level abstractions (eg monads) that would need to be narrower in dynamic languages (eg promises).

And sure, you can couple code and data in static languages, but at least the types will help you when it comes time to change. I've worked with dynamically typed programs where functions rely on some mixture of nested tuples, hashmaps, lists... etc, and it's hard to understand exactly how concepts are represented in code, much less change that representation. If you represent some central notion in your code as some nested primitive type (a hashmap of tuples of ...) and you want to change that representation, you'll still have to update the places it's used in the code, but without a static type system you won't get a list of those places, and you won't have assurance that updated everywhere that mattered. I'm not sure I'm explaining this pattern well, but I've worked in JavaScript codebases where making breaking changes to core data components was basically impossible.

Point being, all the problems you mention come up in both static an dynamic languages. There might be a case that they're more common in one or the other, but it's not obvious either way, and it's going to depend a lot on which specific static type system you're thinking of.