Actually, there are some airlines that also have no assigned seats.
Not calling anyone rude, I'm just appalled at some of these responses. I also suffer from anxiety, especially on planes. But I am an adult, so I have the tools to help myself in a situation like that. I can speak for myself, that my need to sit next to my small children has nothing to do with making my trip more comfortable or convenient. It's simply for safety issues. It's a CHILD-in my case a 1 year old & a 3 year old. The poster who mentioned basic safety, if something were to happen on the plane, speaks volumes.
Personally, if this were to happen to me, I would gladly wait for the next plane or bus (& have done it in the past no problem), before I asked someone to change their seat-it just makes for an awkward situation. I think some of these responses are certainly in the minority of the population though.....or maybe I've just been lucky. When I was very pregnant, holding my baby or toddler, or traveled with an individual with cognitive issues, kind people have always offered to give up their seat for me/them without any hesitation. I've only been in one circumstance that I can recall where I've had to ask & was greeted rudely (a person who took up an extra seat on a bus to place their backpack).
I am also in the camp that the airline needs to take charge of this, to avoid unnecessary confrontations. Put rules in place to protect peoples' basic needs and compensate accordingly, if need be.