Although I agree it's parts of the show and what people want to see, I thought it was in bad taste, but I have a biased opinion. As a former boxer, I know how much a loss hurts. Although I can't fathom the feelings rushing through DC with everything he had at stake in this fight, I do know that after a tough loss you are not yourself for a bit, especially after suffering the head trauma he endured just 5-6 minutes before. When you put everything you have into a thing and come up short, emotions tend to spill out before you gain clarity and some level of control.
While this makes for some added drama and gives the viewer a glance behind the curtain, Rogan is well versed in the fight game and knows you have to protect your own and I pray he stands by his word and never does this again. I'm more pissed at DC's trainer for allowing him to be put in this situation more than Rogan himself though. That is bush league bullshit on his corner's part.
It's likely the first time Cormier has ever been knocked out. I'm guessing somewhere in the back of DC's mind he felt the need to say something on the mic given his role on Fox etc. However his corner at the very least should have got him out of there asap. However I suspect they are somewhat in awe of DC and didn't know what to do.