I disagree because the context here is that they're a streamer. It sounds like there were two goals with the acoustic treatment: (1) to improve sound quality from within the closet which I take to mean echos and reverb and (2) to avoid picking up their partner's voice during meetings. I think it especially makes sense given the closet is in the office where their partner is taking meetings.

Your suggestion of noise canceling head-set only helps prevent her from hearing her partner, not the stream's audience.