I think Hyde's played every game.
In his case specifically, the Packers are generally conservative regarding paying players. His position in their specific defense didn't warrant big money. They've invested in Morgan Burnett and Haha Clinton-Dix at safety. Hyde was relegated to a part time player, mostly nickle corner.
Yes,
1) McDermott said end of half was on him, he thought he could get three plays in.
2) Skirted around it, said they'd have to watch film. However, in post game interviews Lorenzo Alexander said it was on him.
I agree, I understand it's some positive psychology deal. It's fine that he does it, but it's also fine that as an onlooker i find it annoying. I especially found it aggravating after the 3 and out you referenced and did find myself thinking "What the bleep are you clapping about you bleeping bleep."
I think that's the biggest benefit. PR in a round about way. These guys go on local and national shows occasionally and are active on social media, it will serve the team if they support McDermott and the current players.