On the one green is the one area where I tend to notice if someone is overeager from my perspective. Playing too-ready golf you might say. I like people being ready, and I don't have a long routine or anything, but when I'm running through it and about to get over my ball and someone putts 'out of turn', I notice. It feels like a rhythm killer. Doesn't happen a lot, and some of the time it's a situation like the OP mentioned where in their mind they're trying to get done and out of the way for a big putt of mine. I'd rather they just let me putt though. To me it's not like off the tee or on approach because there the other person is in your periphery. On the green they're right in your area of focus. So I try not to be anyone else's guy they notice like that, unless they're really lagging behind.