Yes, educating people was always meant to be a part of it - although I always took this to mean that there was some good, educational, well-presented stuff on there designed to draw people in and gain their attention; rather than expecting them to sulk, sit down for their own good and jolly well be educated!
But the BBC doesn't have a monopoly on educational, informative or entertaining content, any more than the other main broadcasters do.
Channel 4 has Countdown, Channel 4 News, Unreported World and Naked Attraction;
ITV has Mr Bates Vs The Post Office, The Martin Lewis Show, Tonight and I'm A Celebrity;
The BBC has Panorama, Global Eye, David Attenborough programmes and Don't Tell The Bride.
What's the difference? Which of these three broadcasters is the serious, educational one, that must be protected and funded centrally; and which of them is the silly, frivolous, ratings-seeking one that's of no real importance?