I'm not saying that "free enterprise" terminology necessarily harms anyone - its just so dated and vestigial.
It is vestigial, but these things often are. I mean, the same could be said about the label "Progressive Conservative" which is still used by many provincial Tory parties. It dates back to a leadership convention in 1942, when the popular Liberal-Progressive Premier of Manitoba, John Bracken, agreed to lead the Tories on condition that they add "progressive" to the party name, because Bracken's personal brand was heavily tied to the agrarian progressive movement of the 1920s.
The "progressive" part of PC isn't really about ideology, and it's certainly not an accurate description of many politicians who continue to use that label. It's about a deal struck 82 years ago by the Tories to draft one specific man to be their leader. And the way we use the term "progressive" in 21st century politics is quite different from what it meant to early 20th century agrarians like John Bracken.
Hell, Social Credit was like that too. It's named after a weird 1930s monetary theory that they themselves abandoned very soon after they became relevant. The Social Credit dynasty that ruled BC during the Cold War era never even tried to implement social credit ideology or policy, it was entirely a vestige of a brand that had once been popular in rural Canada during the Great Depression.