Sub propellers have a lot of torque. There's no way that one would really get entangled by seaweed. But thick ropes, cables, and heavy fishing tackle are a risk. Every military sub carries qualified divers who could manually cut it free as a last resort.
The same divers who occasionally "inspect" undersea cables. :)
The sub's standing crew would typically have a few qualified divers trained in just the basics. They would only use open-circuit gear on shallow bounce dives for inspections and light maintenance. Anything more complex would require bringing in a dedicated dive team.
If you’re somewhere you aren’t supposed to be, and you have to dive to fix or inspect something, you don’t want to be sending bubbles up.
You’re on your own in the ocean, whether civilian or military, sub or surface. You have to be able to handle any and all potential issues.
Anyway, he was dive-rated. Closed-circuit breathing is the basis of anesthesia machines and has been for ages (at least 60 years). So for us, a closed-circuit system isn't new - it's something we do every day at work. You just have to account for depth. I'd be shocked if he hadn't done it.
Columbia-class is electric drive, which is absolutely wild to me. Those are monstrous motors.
Source: I ran a reactor on a Virginia-class (not USS Virginia, the subject of the article, but in the same class).