Kids aren’t too picky about what they play in. They’ll make do with anything.
Keeping native plants looking like the ones pictured in the article is nigh impossible with children. Keeping a perfectly manicured lawn is also impossible. Which looks best? I don't know? Neither is great in all honesty.
I think at some point if we have lots of kids running around a neighborhood we should be willing to accept the fact that some lawns, whether grass or plants, will just look janky.
If your goal is just to prevent bare dirt for erosion purposes then grass is pretty easy to maintain, even with moderate traffic like running children. Just cut it back every week or two and the lawn will more or less take care of itself.
This plants would get dormant and dissapear into the ground from October to March so will support children trotting around as good as any law for half of the year at least.
And planting native vegetation isn't black and white. You can still have a lawn with plenty of native vegetation.