Re: It's the right badge.
I don’t agree or disagree on your assessment, but I will remark that occasionally restructuring combat units to work together, under a unified command, _does_ make a difference, even if the underlying capabilities don’t change.
https://en.m.wikipedia.org/wiki/United_States_Tenth_Fleet
I’m more thinking of the WW2 ASW* coordination here, but there’s also a cyber angle to 10th now.
Again, no idea if that’s the case here and I’ll even join in a bit o’ cynicism.
* Oh, and no, doubt, early Ww2 USA transport shipping protection practices were risible.