If I'm in those situations and staring at my phone, it's because I forgot to bring a book. Staring into the middle distance while my kid sits on the bench for fifteen minutes and a bunch of kids I don't know ineptly play soccer, or closely watching my 500th hour of kids playing "tag", is a last resort. Hell sometimes I'll just start trying to find weird bugs or something.

I do also play with them, but I'm not one of the parents who's always playing with them any time they're playing, they also need space to figure their own stuff out. Adults can do other things a lot of the time, it's fine.