The thread title and premise is surely a wind up ? Why would any parents with children not old enough to be able to differentiate between drama ie a story - and reality, let them watch Doctor Who ?
Probably the same reason some parents let 4/5/6 year olds watch soaps ie ' The tv is on and there's nothing we can do about it ' ? Not to mention the often distressing lunchtime news plus maybe...in some, cases, raunchy music videos the teenager in the family is watching. Free twerking lessons ! Er...no.
It's not the tv's fault, is it. Record and check if suitable, or watch on catchup, or watch something guaranteed suitable eg a Disney film with the very young child etc. Try the on/ off switch or change channels.
Has Doctor Who ever, been made only, for very young children ? No. Obviously - no. So it's not cast iron guaranteed, to be suitable for every, six year old, is it. Many are, mature enough to know it's about stories. Some aren't. Probably, no one told them.
Who decides who watches what ? The tv ? The child ? No. It should be the parent/parents or whoever is currently with the child.
If a very young child might be upset by any, programme, why is she/ he watching it ? Why aren't they watching things totally, designed for children who don't yet know what fiction/ drama/ pretending/ acting are ?
I'm convinced that a lot of people put the tv on and watch what they want to watch, regardless of the age or level of understanding of children in the room. The adults don't think it's their responsibility at all. It's the tv's fault.
If children watch something unexpectedly, upsetting - why can't adults explain to them why everything is actually ok ?
The notion of children watching something then sobbing inconsolable, in their beds, says a lot about many things but not, about the tv.