I think the issue here is that some kids are acting like jerks and not getting out the way of the car. I mean, where did "Car! Game On" come from? As a kid we played whiffle ball and football in the street all the time. We did it on side streets and we got out the way when cars came down.
All you need to do is get a few of the kids parents to drive by and give them crap for not getting out of the way. This is a parenting issue, not one the city should be worry about.
The exception is on busy streets. It should be a rule already that you just can't be out on medium to high volume streets. That is simply a safety issue. Practically, no one is foolish enough anyway to be out playing touch football in the middle of Reading Road.