In 2002, an ambitious and technically literate BBC technologist pitched a visionary idea to senior bosses for BBC3, the digital TV channel that would be launched the following year.

"Too busy to catch every episode of your favourite BBC3 shows?" the proposal began. "Stuck on the train or bus? Working late or drinking early? Then use 3VOD – BBC3's streaming video-on-demand service to request a recording of any BBC3 programme to watch on the channel's website whenever you like, within the next three days …"

It might seem unremarkable, a nod to the TV and film download and streaming we all now take for granted. But this was 2002; only 43% of UK homes had an internet connection and only 6% of those were broadband. There was no YouTube, no Facebook, no Twitter – and Yahoo! had just tried, unsuccessfully, to buy Google for $3bn. It was a very different time.

The discussion between the heads of BBC New Media over this proposal was not a long one. The idea was largely laughed out of the room, with what now seems the damningly short-sighted comment that who in their right mind would ever want to watch telly on a computer. That this would eventually lead to high-definition, long-form programmes on a 40-inch plasma TV was unthinkable – and these were the people at the BBC paid to explore and exploit technology to serve licence-fee payers.

Fortunately, those with the real vision and technical understanding had the persistence to match.

They began, using the permissions BBC3 had been granted in its service licence, to build up the service from 3VOD to the iMP – the interactive media player – and eventually the iPlayer. In BBC legend, it took 84 internal meetings for the small team committed to the iPlayer to bring the idea to fruition.

By March this year, corporation bosses had decided to ditch what they saw as the peripheral BBC3 digital TV channel. The headlines were failure, closure, savings … tagged on was that the BBC3 content would still be available online.

But this was a service designed for 16- to 34-year-olds, a generation that lives online. Why did management ever bother putting it on TV? Why did they not recognise that properly serving BBC3's core audience for the future would mean delivering content online?

The technologist behind that proposal could see that in 2002. It took BBC management 12 years to catch up, and even then the announcement was defined as loss of a TV channel rather the chance to be digital first.

Is it a good thing that a very early idea for a very early market opportunity was not explored by our public service broadcaster? Is it a good thing that the space was instead left for commercial organisations to explore, and that the denominator for the BBC's ambitions was the conventional mindset of its executives? I'd argue not.

The BBC was founded on exploiting the breakthrough technologies of the day to achieve the public service aims of education, information and entertainment.

There have been stellar examples of this, even quite recently. BBC News Online set the standard for what was possible in online publishing for years before commercial rivals found their feet. iPlayer too brought catch-up TV to the mainstream, developing a public appetite for it. The engineers and technologists that built News Online and iPlayer moved on to startups and the wider tech industry just as they should, talent trained at the BBC.

But what has happened since then? The badly handled BBC3 announcement is indicative of much bigger problems at the BBC. Many people in the UK still feel deeply committed to the principle of a public service broadcaster, and there is no small amount of affection and nostalgia for an organisation that, to some extent, reflects our national culture, our identity, our public discourse.

Or it should do. This broadcaster – or whatever a broadcaster becomes in the internet era – is beginning to fail us.

This is far bigger than a lack of technological strategy. Journalistically it is feeble – too terrified to follow up the NSA/GCHQ surveillance investigation by the Guardian, yet festering with articles such as the four-sentence report on a toddler whose head got stuck in a toilet seat. Creatively, it seems defunct and derivative – When Corden Met Barlow anyone? Politically, it has no standing at all, and no one able to stand up to political intervention and the increasing threat to the licence fee. Whoever replaces outgoing BBC Trust chairman Lord Patten will play a key role in determining the future of the licence fee and charter renewal. But no one person can answer the question: what does the BBC do, and who is it for?

What should a 21st-century public service institution with that Reithian purpose really look like?

And if it were created today, would such an organisation be anything like the BBC is now? Once, it might have been enough to get those visionary engineers back in the room, but now the BBC's problems seem far more pervasive. This is our BBC. Where do we start?