Many commercial dishwashers might be specialized for certain dishes, so adding a straw washing machine would be a significant expense. In addition, I've heard that many commercial dishwashers require the dishes to be scrubbed beforehand (see https://www.webstaurantstore.com/guide/620/types-of-commerci...), and straws are quite difficult to scrub.

Given that most restaurants that go through a lot of straws want to provide the option for takeout anyway (for which you can't use metal straws), it makes sense that most restaurants don't bother.