It is seldom that a family is split up after buying fares with assigned seating. If that family gets to the gate and checks in early enough, it just isn't an issue.
I do know that there was one time when I was flying SW. It was before the current boarding system came along. It was the old system where you had to get there early and sit on the floor in the appropriate line. First come, first served so to speak. So, we were there, about 8th in the A line. There was a woman who was wandering around the gate area with her young son..about 6 or so. She never got into a line, I figured she must be waiting to board another airline.
Imagine my surprise when we were all boarded, no one else was coming, the FAs were getting ready to close the door. A gate attendant came up and told them to wait, there were two more passengers. It was that woman and her son. And, of course, there were not two seats together...plenty of single seats though. The FA made an announcement that they wanted someone to move so that the mom could sit with her ds. No one moved. The FA announced that that plane wasn't moving until that mother was seated with her child!!! Finally someone moved, away from his traveling companion, and sat by himself in the back of the plane. the mother and son were seated in about the 5th row, with that nice man's wife.
For the vast majority of flights it isn't going to be an issue. No one should be worrying about being seated away from their kids. I do know that my dh got to Logan early for his (and our dd's) flight to MCO, only to find that the flight had just been cancelled!!! Jetblue was able to get them seats on a flight that was boarding at that moment. They flew to the gats, barely stopping at security. My dh explained to dd that they may very well have to split up..she wasn't happy but that's life. She was 11 at the time...fully capable of sitting by herself on a plane. Nice thing was there were two seats together so they didn't have to split up. And to the best of my knowledge, no one was asked to move to accomodate them.
I just get tired of the sensationalization of this whole thing. Fly with an airline that allows you to choose your seats. Be sure to continually check on those flights and seats before you are due to leave...I check weekly for the months before and then every day for the last month...just to be sure. Checkin as soon as you can. Use online checkin if possible. If that isn't possible, get to the airport as early as you can and get checked in. It's not rocket science.