Those Sony headphones do processing to the signal regardless of whether you're using wireless or a 3.5mm. They can still make sound with no power but it feels more like a backup in case the battery is dead. It seems like a sensible design decision given that most users will want them turned on for noise canceling even if they're wired.

That's his point. They're using the device's DAC when wired which is why it doesn't sound as good as when using Bluetooth through the headphones' DAC.

Sure but that's an issue with wired headphones in general, not specific to these.

I mean, I'm pretty sure that DAC on my MBP is better, but it does not fit those headphones well.