One thing I haven't heard mentioned.. is that kids don't get to choose what kind of parent they have or what kind of risk/reward choices that parent makes. It is my strong belief that kids change the game. When one becomes a parent, one is obligated to prioritize the children's interests.
As in most things in life, this becomes a question of where to draw the line. No one lives risk free.
My opinions: Soloing with kids is beyond the line. Leaving a child parentless is an unacceptable risk for the benefits of soloing (which I don't discount).
Sure, people get hurt on gear, but gear saves many peoples lives also. Things can go wrong: Bachar has a accident with a weak arm, a German woman solos on an unknown route, a snake is in the hold, a rock breaks off. Not all is controllable.
With the variability in judgment, experience, gear, conditions, psychological state we need a community that encourages and promotes safety. And I think safety should be a primary factor in decision making while climbing or mountaineering.
As for the lines of people on whom others don't depend, well...like I said, a good thread. My personal advice is not to solo... much.