Why do “Actors’ Directors” like Sydney Lumet, Mike Nichols, and Martin McDonagh so rarely win Best Director?

An Actors’ Director is one that elicits raw performances from his or her cast, and often they’ve got a background in theatre, but it seems they’re frequently snubbed despite sweeping cast nominations.

Sidney Lumet never won a Directing Oscar, and Mike Nichols only won one for The Graduate.

Martin McDonagh yielded four acting nominations for Banshees of Inisherin and three for Three Billboards Outside Ebbing, Missouri, but has only been nominated for Best Director once.

What about this particular style makes it so unappealing for Academy voters despite the obvious results in craft and believability of the resultant film?