I don't understand what you want and what you don't want? You want specialization, because you don't want to buy other people's goods?
"YOU CANNOT progress unless..."
This isn't true, and after your caps lock declaration you point that out. But beyond! your two examples let me add, you will have extreme difficulty HQing items. But it's not impossible. And there is plenty of money to be made in NQ items. If someone wanted to be just a weaver, they could totally do it.
Your example of Terminus putty really confuses me? It highlights the fact that we already have specialization. (Lots of people are 50 without alchemist 50 or alchemist master book 2.) And Terminus Putty is also the poster child for why people want this change. People are arguing for that lack of omni craft so traders have to trade with other traders. You could certainly buy all matts, and only make end product and make gil.