For me, even though all the info you've given sounds beyond wonderfully safe... the deciding factor would be that while she is at the playground, you cannot see her. She would be alone. If some stranger drove through, you wouldn't know. But they would see her alone. It only takes 5 seconds...
Or what if she fell off the swing and got hurt? You wouldn't know. In that exact same situation, if she had a sibling or friend with her, that could call for you or come and get you... that would swing the balance to letting it be okay for short park visits. Alone, I'd say no.
We too live in a very safe neighborhood: closed end neighborhood.. no thru street, gated entrance off the main road..(3 miles off the interstate out in the middle of nowhere EXCEPT for the interstate being there). We know every person in our neighborhood. BUT, if my youngest (now 9) wants to ride her bike around the block... I want her brother to go too... if she were to fall and get hurt, or she were to get injured somehow, (woods on 3 sides of the neighborhood, and have seen wild hogs, deer, foxes and even bobcats wandering around a few times in the 4 years we've been here, plus stray dogs and of course snakes) and she were to get bitten, or whatever else... I want a second person available to go for help.