Only an empty platitude if one interprets it as meant for those laid off. But if you think about it as a message to remaining employees, the board, and to shareholders, it isn't an empty platitude at all.

Perhaps but even then it's still pointless. Over-hiring was a strategy to take advantage of easy money and layoffs are a strategy to clean it up when the well runs dry. The very act of laying people off indicates that you are taking responsibility for changing direction.

That said, when someone says they're taking full responsibility there's an implication that they're going to take on pain or consequences. I don't say I'm taking full responsibility for washing my car when it gets dirty. Not saying he should be fired or take a pay cut, just that he said something dumb and did a terrible job of reading the room.