but these errors are usually so trivial, that any good integration test would find them any way...
You don't. Even 100% coverage isn't enough to map all the potential issues with incorrect types being passed around.
Types are a highly compact way of adding tests and documentation to your code that automatically integrates with everyone's IDEs and your CI pipeline. I don't know why you wouldn't use it if you think these things are useful.
"No thanks, I'd rather spend all my time writing these things I could write much faster using simple types."