I'd always have grease in at least two places, in case the umpires would ask me to wipe one off. I never wanted to be caught out there with anything though, it wouldn't be professional. ↗
People come out to see the players. When do you see a manager anyway? When he's out on the field arguing with the umpires, making a fool of himself and you know you can't win, and when he brings out the line-up card. ↗
It turns out umpires and judges are not robots or traffic cameras, inertly monitoring deviations from a fixed zone of the permissible. They are humans. ↗