Diversions are common but never routine--no matter what they're high workload (especially with the short timeline in this situation). As a pilot I'd interpret it the exact opposite way--recognizing that they're in a high workload situation and shedding unnecessary tasks could be a sign that they understand their capacity and how to manage it well. It may be true that a more experienced crew might be able to manage more at the same time, but recognizing one's own capacity is something that is far more difficult to teach. Sterile cockpit rules were borne out of accidents stemming from pilots who overestimated their ability to multitask.

(And that doesn't even address that, across the entire event, the pilots spent the vast majority of their time in phases of flight where they were specifically prohibited from making non-safety-related announcements. While we don't know when they decided to divert, we do know that only 6 minutes passed after they left the hold before they had to maintain a sterile cockpit until they were, more-or-less, stopped at the gate.)

Edited to add: I imagine that the reality of it is probably far less dramatic too. There's a solid chance that talking to the cabin was on their to-do list and by the time they finished the tasks that required immediate attention they were below 10,000 ft. and just ran out of time. (I mean, it's possible that they just didn't care, but I think that the circumstances warrant giving them the benefit of the doubt.)