Oh yes an enclosed soft play centre is different-after all, they ARE enclosed although I do say "do keep giving me a wave" and I don't sit with my head in a gizmo/book/paper either-I discreetly observe what's going on. One DGD was backed into a corner by two "madams" who had gone into the younger children's area. Poor DGD looked most unhappy and then relieved when i turned up.
A public park is very different IMHO-this one was quite large, very busy due to lovely weather, so I just trailed round after her.
One of our dear SILS was prison officer/police officer. When he and our DD1 had our first DGDs, now early twenties, and we had them most days, he said very kindly but firmly to me "never take your eyes off them for a second" esp in parks as it is where predatory folks prowl. As I say, I think I'm just doing my job, looking after them but not restricting fun.