Something to also take into account is that there are no programmes intended for 8 to 14 year olds shown during prime time on the main channels. Almost every programme shown during prime time is produced with entertainment for adults in mind. Children's programmes shown during prime time are on dedicated channels.
How many people on this forum are seriously interested in documentaries, educational programmes, and even highbrow arts, or is mass entertainment the interest of most users?
There are no programmes intended for 8 to 14 year olds on the main channels because they're on dedicated channels. You just said it yourself. If they were on the main channels during primetime, then adults wouldn't watch. 8 to 14 year olds would be, in theory, on their computers or smartphones. Alas, low viewing figures, no ad income, everybody loses their job. That's why it doesn't happen.
Like it's been said many times, this isn't how commercial television works. Nobody can afford to have a "dedicated TV channel with a tightly focused audience" because it doesn't make money. The majority of channels that broadcast today don't necessarily care about entertaining the audience, they just want to make money, which is why the aforementioned factual channels have broadened their programme library to include more general entertainment programmes. If LWT couldn't manage high-brow programming back when competition and ad revenue wasn't as much of a hinderance as it is today, what makes you think it'd work now?
And whether we are interested in "documentaries, educational programmes, and even highbrow arts" is irrelevant. There are niche programmes I like but I know it'd make no sense to have them on at primetime on a mainstream channel. More to the point, there are various other mediums which you can consume content through. So if you think you'll validate your point by trying to uncovering our personal tastes, it won't work.