I love to see my horse expressing himself in liberty! So yes I stay with him and take pictures of him :)
I think liberty is a good way to built or improve your relation with your horse. You can stay with him and play or work a little bit (he follows you for example).
I do, everyweek. Sometimes I stay with the horse, I play a little bit with him, sometimes I don't have time so I let the horse with a ball or with another horse, it depends.
When I can, I let some horses of my equestrian center in the inside arena. They love that! They can unwind and I play with them. We run together, I try to teach them some tricks (count, smile, grab that, follow, backwards) :)
Once a week I try to let him in the inside arena. Most of the time I stay with him as I know he gets bored if I let him alone. We play a little bit, we cuddle, he goes a little bit crazy, it is really funny to see!
My horse goes to the paddock everyday. It could be fun to stay with him but I actually don't have time so I let him alone. He enjoys the
lush grass of the paddocks!