Joseph:
I can confirm that I have never seen a short-jacket, yeshivish father walking alongside a kid with a bekishe. I was talking about young kids as in ages 6-9 roughly.
I don’t assume that these kids are going to keep the peyes forever, especially when their fathers don’t really hold of it b’shittah. I interpret this as a kind of kids-only minhag, which is weird. Harmless, but just a wee bit bizarre.