I work at a standing desk and I love it... I almost never stand still, though. I dance and pace as I'm thinking and get to bounce around and be a lot more active than when I was in an office chair.
When I need to stand for a thing I will inevitably fidget. I don't frequently need to stand stoicly (I don't have a job that requires me to be the silent background or anything) so it's not really an issue for me. Pace and enjoy it.. if you're in a museum it's actually kind of awesome once you realize you can pace and get different angles to view things from and, every once in a while, you'll hyperfocus on something and just dead stare it... but it's perfectly acceptable to pace and fidget as an adult.
I'd also mention that I think the constant need to fidget is actually a long term health super power - it's unhealthy to maintain monolithic postures for extended periods of time - moving is healthy and micromovements keep your body on constant motion.
Yes exactly, that's how I think of my standing desk too (and I thought that was the whole point of them). You're not actually standing at them, you're supposed to move around. Standing for too long is uncomfy, so a standing desk makes you move around more as you start to feel less comfortable standing in one position.