I disagree; the communication aspects - including external - are a hugely important part of any incident response. IME the biggest challenges in these situations are the many levels & combinations of communication and coordination. You don't need your best DevOps person doing it, but there should be plenty of competent technical product managers or engineering managers who could do this well.

And how do those product or engineering managers get information on what’s being tried and what is being discovered without slowing down the process of fixing the issue?