It matters because the party has some methods of coercing a rep. to vote with the party (lack of access to the caucus, fundraising, joint marketing, etc). The switch removes that pressure, so I’d bet we’ll see her vote with conservatives even more now since there’s nothing for her to lose.

And, most voters don’t know what a rep does, only who they caucus with, so this will really matter at the next elections (whereas staying with the Dems might have still allowed her to win if she got through any primary challengers).