API calls and processing, conditional display logic, formatting, error handling, form and data validation... all of those things fall under the rubric of "business logic" that lives on the client.
Besides, if you believe that all of those things should be in the "back-end", then what are you doing with Flutter? Just write a server-driven web page and be done with it.
It sounds to me like you assume that new technologies are somehow superior simply because they're new. Flutter is just code, right?
And for non-trivial projects, you still need development teams to write that code, QA engineers to test it, back-end developers and DBA's to support it, UI/UX engineers to design it, PM's and PO's to decide requirements and business priorities, and so on.