In my experience (6 companies, variety of verticals), COO responsibilities really vary. I haven't encountered a COO who wasn't interested in improving performan

In my experience (6 companies, variety of verticals), COO responsibilities really vary. I haven't encountered a COO who wasn't interested in improving performance, but I also haven't encountered a COO whose role could be described exclusively as "business optimizer." On the other hand, I've seen BAs and PMs do the kinds of things you describe, along with plenty of engineers. I've also seen people doing those things who have vague made-up titles unique to the org. In some cases, they were hired for something else, but then ended up what they were good at, and instead advised company leadership. All of which is to say: if you're looking for a career where you can do more of that kind of thing, you might do better focusing on organizations rather than titles.