Solid UX people think like product people, but you either over-burden them, have them shift part of their roles off to others (research, user testing, etc),or do both jobs poorly. Good product people not also doing design, research, technical work, etc...they should be able to manage several teams / projects in a related area at once.
This all sounds nice, but developers/designers rarely want to do PM work. The PM position is as much a creation of developers who don't want to interact as it is management.
Even developers that do don't want to spend all day in meetings. A PM can help there.
When they realize it's more soft skill oriented, endless meetings, power point deck after power point deck, stakeholder after stakeholder, and 1 hour left to code, they finally get the picture.
I was once that developer, thinking I knew what was best for everything. I scoffed at management and project managers. Now I know the real truth - their job is way harder than it seems.