To go at it from another angle: I'm working in a relatively large Java codebase that also likes to pass around generic ad-hoc data-structures such as maps. And I'm having exactly the same problem problems there. Static typing does nothing to help the situation.
I realize that data-oriented programming is more likely to happen in dynamic languages. But correlation is not causation.
IMHO Static typing => structure,
not necessarily Map<String, String> (which is also a type).
Shaping data is quite important and having an associative array doesn't necessarily means that the data is shaped.
Right. . . but, way up at the start of this, you specifically called out using associative arrays for all your data. And what I'm saying is that, while that's absolutely true, it's also technically an orthogonal question from whether you're working in a dynamic or static language.
Yes, sure, we can say that no true Scotsman would use a static language that way. But I think that's maybe missing the point. If you can dismiss this practice in static languages by just saying, "Well, maybe you shouldn't do that," why not also apply the same dismissal to dynamic languages?
That said, there's a specific subset of dynamic languages that make it more difficult to do your domain modeling any other way. Clojure and JavaScript belong in this group. I'm not sure of other examples. Basically, if the type system has been set up such that everything is either a map or a glorified map, you aren't left with a whole lot of other options. But not every dynamic language does that.
In Python, for example, I always use dataclasses for data. As long as I'm being good about this, I don't actually need to explicitly write unit tests to verify that types are being handled properly. MyPy's got my back. And, even if I'm not using it, unit tests for covering actual behavior will typically blow up with a type error in about the same amount of time that it takes a static language's compiler to detect one.
Yes, all dynamic languages have this problem. I have transitioned to statically typed languages and it has been very peaceful so far :)