Same here - since I often walk among riders I tend to go to my push cart, put putter / clubs away, and mark my score while watching anyone else putt out. My purpose is to be ready to go once everyone is done so I don't hold anyone up by being a walker, but I agree I wonder if others find it rude.
I’ve been rolling with the lsw strategy. Aim at center of the green much more often than I go at the pin. Certainly helps me hit more GIR and intern more pars.
but, I just feel like there is more to this. More to identify when planning my approach. There are definitely times where aiming the center of my shot zone somewhere other than center of green is beneficial. Indentifying problem areas in advance. Being able to identify an easy chip vs. a difficult chip. Etc. etc.
I find this thread interesting. Now that tending/replacing the flag isn't a thing anymore, I tend to putt out and walk off the green (usually to my push-cart, since I try to walk whenever possible)...I try to watch the remaining players putt out, but not actually wait for them on the green.
It always feels odd, and I always wonder if they find it rude.
Many times, I'm the only walker in my group, and the "head start" helps me get moving towards the next tee to match the pace of those in carts. But, it still feels weird and I tend to make sure I'm looking back while they putt.
(EDIT: this is all in casual play)
We are talking about Tournaments and competitions, not casual play. I understand the idea in junior golf of the first player holing out and going to the next tee AND teeing off to assist pace of play. To me, once one is an adult and playing in a tournament, one stays around the green because one is marking for another player.
In casual play, I have no big issue with a player moving to the next tee before I have putted out as long as they are not making noise or moving in my field of vision.