I've now listened to the second of Peikoff's Eight Great Plays lectures. This one concerned Othello, and includes a recounting of a long-ago discussion with Ayn Rand about this particular play.
Rand, in his recounting, sees the key to Shakespeare in the line "What fools these mortals be."
As a side note, this line is mistakenly attributed to Ariel, in The Tempest, in this lecture. It's actually Puck, in Midsummer Night's Dream. I'm not sure whether that's Peikoff's or Rand's error. I'm not sure it matters. Puck is a fairy, and Ariel is a spirit, so I guess neither is a mortal.
Anyway, Rand sees Shakespeare as Olympically detached, and not giving a damn about his characters. She thinks she's a great artist, but she loathes him.
Peikoff, however, clearly does not loathe him. Peikoff sees Othello as a play that will improve your life because it provides such an exquisite experience, even if it will depress you for days.
Shakespeare does sometimes express Olympic detachment, but I wouldn't name it as his basic attitude toward his characters. I think that's unjustified.
And perhaps I should add, it's his characters that sometimes express Olympic detachment. One of the difficulties in interpreting him, is that all of his characters express their ideas so vividly, but it is hard to say which characters speak for him, if any.
Perhaps one could look to his sonnets, where he speaks in the first person, to begin with a basic assessment of what he, himself, really thinks.
He had a way with the striking phrase,
and shifting views can leave you in a daze.