All good points, I must say, but why does it have to be an enemy sub that could potentially track and take down the screening sub? Having one more source of noise means that not only is your CBG more exposed to passive acoustic sensors but your enemy could not more precisely track the defending assets. After all, submarines that are slated for CBG protection would still have to "fight it out" with an attacking asset, and the fact that it is louder would place it at a disadvantage. I'm not sure how big of a difference the carrier's ASW screen would make since any attacking force would have supportive naval platforms of their own.
Personally I don't think any nation should compromise sub acoustic stealth for the sake of faster development.
You compromise sub acoustics in order to have some submarines when you need it rather than no submarines at all.