To the poster who said "if not just pay at the airport"
Pay for what? If a Check in agent tells you there are no seats together left on the flight there aren't any. You can't pay for seats that don't exist. We don't the magically find some seats together just because suddenly you want to pay.
The only seats payable at the airport are Emergency Exit seats if they've not been pre booked. These seats can only be sat in by people who confirm they are "Fully fit"and able bodied and comply with other questions". Children cannot sit in these seats although the age restriction will vary from airline to airline and between aircraft type. The youngest on certain aircraft with some airlines is age 12 but can be upto age 16 with others.
As explained before, we won't move pax that have pre paid and booked in advance. So sitting a whole family together who've not booked is unlikely in peak season. You could ultimately end up with 1 parent sat next to 1 or more younger children, but next to can include different rows with a parent sat behind or infront of a child or even infont if 1 child and behind the other. We try for better but pax who pre pay to book are also valued customers we want to keep happy and respect thier booking. We really do try our best. I get no satisfaction from splitting families up but sometimes, well often, it actually is our only option.
Moving pre paid pax is an absolute last resort and will only usually be a free upgrade to the emergency exit as a way of saying thank you for thier inconvenience and I suppose a sweetener to encourage them to move. However, we can only do this if the seats are still available. They usually get booked up early when people pre book thier seats. Also children, elderly or pax that are not fully fit cannot sit there by law and in peak summer it's not always possible to find suitable people to move there as most families want to sit together.
I'm with most people in that I personally hate the booking seats thing as I'm a mum who travels with kids but if the reality of worst case being sat directly behind/infront of your young child is not something you are comfortable with, then just play the game and pay up in advance.
Ground staff are responsible for seating. Cabin crew are under no obligation to sort seating issues other than for safety reasons and cabin seat changes before take off cause all kind issues including delays, especially those done without cabin crew being informed.
Hope this helps explain a little how it works and how we do actually try our best to help everyone. There are other factors we work with too such as people with disabilities, infant oxygen masks etc. There a lots to consider when seating everyone.