I couldn't from that quote understand Knuths view.

I have however the impression that some distractions of life are more fundamental than others. If the distraction is that you might not have food tomorrow or you fear for your safety, indeed I doubt you can focus on research. However other things like babies crying and "responsibilities" are only a distraction if you let them. My mental model is that "doing research" is somewhere is Maslow's pyramid which is not the bottom, but it's not as high up as most people would expect either. I'd like to hear other people's thoughts.

No, a baby crying is often a duty. If you’re the only responsible adult, you need to deal with that. The only people who get to dodge that responsibility are ones with very supportive partners or enough disposable income to pay for a nanny.