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I was my wife's caregiver and dad to 5 young sons over 20years. I was the sole parent taking them to playgrounds and other outdoor activities, upwards to 200x a year.
In all those events, I never experienced nor witnessed anything remotely like what you described. Not for me and not for any other solo dad. On rare occasion, I was complimented for spending time with them. That's about all the notice I got.
Well, it certainly puts the notion on the table.
Let's run with that. Let's say that qualified folks have evidenced this phenomenon; we've learned there are regions in the US where playground dads are routinely considered to be dangerous to their own kids (and presumably kids in general).
And it's not universal. This indicates there's some strong social effect that can be tightly limited to a region - be widespread and pervasive in one region and fully absent in another.
What sort of effect could mass-mold minds across an entire region yet still be so geographically limited?
If the judge wasn't convinced in the anecdote when it was his job to figure it out with his career on the line, we have no right to assume that the judge got it wrong, without additional evidence. Feigning victimhood is a popular sport.