"Too much traffic"
I agree that all interviewers should be thoroughly steeped in the work as much as possible. But I disagree in part with Iyer, particularly on the point with Sontag, who comes across as a rather impolite person in that anecdote. While I do my best refrain from asking personal questions of authors (unless it pertains to a memoir, in which case the personal is tied into the work), what an author does or says outside of the text is sometimes as important as what's within the text (or helpful in elucidating how a quote pertains to a working method).
Yes, it's a difficult balance to strike, isn't it? I think Iyer means Sontag to come across as impolite, only he doesn't quite want to say it. I interviewed Margaret Atwood a few years ago in front of a lot of people (I was a last-minute stand-in for a far more distinguished colleague who had to cancel), and I was pretty nervous about it beforehand, only of course she was absolutely lovely: but you often want to start with an observation culled from an essay or an interview or something like that, it is not always going to be so interesting for the hundreds of people in the audience to hear discussion perhaps of a novel they haven't read, etc.