i dont ignore them all the time, far from it, but if i take them to a park i will let them get on and play, they dont need me to play with them, infact i think its better for them to build up a sense of independence and get on and play tbh, they are capable of a lot more than we give them credit for.
i wont allow them to be rude or badly behaved, but i will allow to get on playing in what is a PLAYpark. i will tell them to share/take turns as necessary and keep a watchful eye on them, but they like to go off and explore and sometimes make friends. my ds2 inparticular is actually great at befriending little ones and will push random children on swings, roundabouts, be the first child to help a little one who has fallen over etc.
we do plenty of other activities where we play with them, the park is somewhere for them to run around and have fun with minimal input from me, tho if i feel like it we may play football or frisbee and i will push the little two on the swings (big ones dont need me to) on the whole tho i watch and give assistance when needed, even with 19mth old dd i dont follow her around the whole time, i stay near enough so i can help/interven if needed, but she has 4 older brothers to watch and copy and they will also help her if need be, she often doesnt want my interference she wants to do stuff on her own.
the child was on a roundabout with another child, hte op chose to push and she chose to play trains with them, they woudl probably have been equally as happy pottering around playing trains themselves, and as i said if you or your child wants to play alone, then the park isnt the place to be.