I like this explanation.
I'm biased coming from UX, but I think the value is in the isolation of focus. If I'm less concerned about the business goals than the product designer would be, I'm more apt to advocate for the user in a team based setting. Product, UX, and engineering trade notes, and even if I'm overridden, at least that perspective was considered.
I've seen UX used more in large companies while UI design/visual design is more visible and requested by all kinds of teams.