Uh... aren't you leaving out product managers? Is a "product engineer" just a glorified term to get an engineer to do two jobs at once?

CEO: "We need a search box"

Product Owner: "Okay, let me do some research and build out a design. Here are all the metrics we'll track and quantify the success of the project on"

Engineer: "Okay I've implemented your design, and put in all the essential logging to power those dashboards"

Product owner: "Great, after our search box, sales went up 7% for these items. This means $75,000 a year. Success"

CEO: "K."