I first thought that what you mean by "move around" is that they would turn around depending on whether some public transport is approaching the stop or not. The platform pictured in the cover image looks like specifically designed to have a little green barrier in the back to distance the people sitting there from the street. Such barrier could be made way bigger/thicker, for example - a high green wall. That way the people sitting there would be separated from the street view, noise and smell at least to an extent.
When some public transport would be due to arrive, the platform would turn, allowing the people sitting there to access the street. When the public vehicle left, it would turn back again facing the sidewalk. Apart from serving the function to distance people from the street, such turning stops would at the same time inform the travelers about the approaching vehicle in a rather playful way. The platform could start blinking, making a sound, or otherwise signaling before turning around so that the people would know and won't climb on or off it during the turning. There could also be "gates" that would close before the turning and open after it.
One serious drawback that I see is if such stops were near the streets with very frequent movement of public transport the platform would have to turn back and forth very often, especially during peak hours. Maybe it would be rational to install such turning bus stops near the streets with high traffic but rather little public transport movement (e.g. - near busy roads that are further away from the city center).