The right answer for any leader at Director or above is to simply schedule 1:1s with random people from all levels of those you manage directly or indirectly, at least once--if not more--per week.

It's a rather efficient bullshit detector when you have two or more layers down in the organic chart.

I guess I didn't mean to criticize managers who are continuously soliciting feedback through a middleman, just ones who aren't soliciting feedback at all.