It's important who controls the money of the Dem party and how it's spent. Ideology will of course impact that, but I find it weird that the Dem choice of DNC is important because they're the "face of the party" or because someone in Fritters will decide their vote based on the perceived cultural and identity affiliations of the DNC chief. I'd be shocked if the name recognition of DWS nationally ever rose above 20%.
Mostly, it's about which Team controls Democratic DC and directly and indirectly controls much of the massive amounts of money which flows through the Dem party industrial complex. Likeminded people putting likeminded people in positions of behind the scenes power.
All of that matters, just not in the way it's usually talked about.