I agree with all your individual points but I’m slow in understanding your overall message, sorry.
Or go work for a company that makes products. You will learn a whole lot of things about bringing a product to production that you will not learn at pretty much any product development consultancy.
Note that right now in 2022 just about everyone is desperate for help. Be sure you like doing parts substitutions.
I've hired layout shops where we worked with the designer more or less directly but at "whole product" design shops, if they even have a layout designer, in my limited experience it's not usually a customer facing position.