I thought they were going to bring in bard girl to sing and lift everyone’s spirits, but I thought this worked better.
I was thinking that too initially, but you're right. This definitely worked better. At first his speech sounded... terrible. But then I realized it was actually perfect for Subaru. He's an ordinary person with few redeeming qualities. He has nothing special going for him except Return by Death. He was basically saying, "I'm a weak and pathetic person but because there are people I care about I will fight and I will win. B-T-Dubs, I also killed a Sin Archbishop. Did I mention I'm weak and pathetic? What's your excuse?"
What happened to “Don’t tell the Sin Archbishop your name?”
I'm guessing Gluttony has to know the name and face of the person to eat their existence. Subaru's name is already well known so just saying it again shouldn't be a problem.