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.