Great perspective and great way of putting it all together, Tommi.
One thing that a really miss in every discussion about product is: how it is supposed to interact with the big picture in a company. Considering "big picture" all the areas outside the boundaries of competencies like design, technology, data analysis, etc.
How product managers could break the cycle of demand/deliver that many companies establish between a product team and other areas involved in business.
More than represent their interests, how could a company design it self in order to promote a more "product oriented" view within all its different teams.
Maybe it's a good topic for a future post :D