Is secondary 120/240 distribution line wrapped around neutral' dangerous?

I assume what you are saying is that the secondary, which is typically a twisted triplex cable, of two insulated conductors and a bare neutral conductor (for single-phase, secondary distribution), is strung below a bare neutral for the primary distribution, which also runs between the poles, below the cross arm. And you have noticed that in some spans, the primary neutral is missing and you surmise that the secondary neutral functions as both a primary neutral and secondary neutral. Your assumption is likely correct.

I have seen this a few times, and it always strikes me as odd, but as long as the system is fairly well balanced, and/or lightly loaded, there would be no problem. In many systems there is a ground at every pole or every few poles that bond, or ground in common, both the secondary neutral and primary neutral, to a grounding electrode (ground rod or plate) at the base of the pole. In effect, both of these conductors are securely interconnected throughout the system. I doubt if this would cause a significant lightning hazard becuase, as I stated, the system should be very well grounded.

What if the primary neutral getting disconnected from its upstream pole and then using the downstream secondary neutral for its return path? The current would use the only paths available to return. Those would be via the secondary neutral and to the customers' grounds. This could energize metallic plumbing and set ground voltages to above 0 volts due to normal ground impedance.

Couldn't this be a danger to the three toddlers and or the dog that lives in the house?

The picture with Born Yesterday looks exactly like what is on my house and I don't see how you would think there is a greater lightning danger from one arrangement or another.