alt Hacker News> PMs should be able to clearly form a customers' world model, fit that into their business, and clearly articulate needs to the "builders": UX designers and software engineers
What your describing fits a job I did many years ago and my role was distinct from that of the PM and my job title was Business Designer. That was in the context of software that required complex and precise specifications so may not be typical, but I do think running a project and understanding customer needs are different skills.
Depends on your "business moment" (how mature you are, how complex your product is, etc) if you want to have more specialization or less.
Most software teams benefit from getting daily access to someone who deeply empathises with customers and understands how can their challenges translate into business wins, especially when the problem space is still being explored.
Note that I am referring to product managers, and not project managers (since you bring up projects).