The BBC’s announcement that it will close three of its linear broadcast channels – BBC Three, BBC Scotland and Radio 4 Extra – makes sense financially.

BBC Three’s most popular show on Monday night was a repeat of an old episode of Top Gear. Around 77,000 people tuned in.

BBC Scotland’s TV channel was watched, according to this year’s annual report, by a weekly average of 12% of the Scottish population. Scots simply aren’t tuning in in the numbers to make it cost-effective.

(Fascinatingly, BBC Alba, which is aimed at Gaelic speakers and learners, reached 43% of Scots weekly – was it boosted by its rights to broadcast Italian football’s Serie A, with the commentary mainly in Gaelic?)

It’s hard to argue – although no doubt some will – that there is a business case for keeping BBC Scotland’s TV channel open.

The same goes for BBC Three, although the hokey cokey that has gone on with that channel – launched to fanfare in 2003, later made digital-only, then brought back to linear in 2022, now back online only again – has looked indecisive. Bizarre even.

But the bigger picture is that viewers and listeners are already migrating online – increasingly finding the BBC’s programmes not via those linear TV and radio channels but on iPlayer, BBC Sounds, and, more recently, YouTube.

So that’s the business case – and the BBC needs to save £500m over the next three years. That figure is concentrating minds.

But axing the three linear channels is a drop in the ocean financially. I understand it will save less than £10m in total per year.

Last year the BBC spent £42m creating content for BBC Scotland. It still plans to create many of those shows for iPlayer – and BBC Two in Scotland will be reconfigured to deliver Scotland-only programming.

The part of BBC Three that commissions programmes will actually get more money to spend on creating content aimed specifically at 16-34s (with a core focus on the 16-25s).

This was the network that commissioned Normal People, Fleabag, Killing Eve – programmes of quality and wide appeal.

There’s also been a recent announcement of commissions dreamt up specifically for YouTube – to reach those 16-24s who the BBC (and other public service broadcasters) find so difficult to lure to their own platforms.

Many of Radio 4 Extra’s programmes will also still be on BBC Sounds. If you listen to the Daily Service, first broadcast in 1928 and the longest-running programme of its kind anywhere in the world, you will still be able to find it.

So these aren’t major cost savings. The BBC would likely argue, when it comes to audiences, who are at the heart of everything, it is pivoting to find them where they already are.

What’s been announced today is more about the direction of travel. It’s about the continuing evolution of the BBC, a streamlining as audience habits change.

That doesn’t mean it isn’t painful to all of us inside the BBC. Job cuts are always difficult. In News, 100 more roles are being axed. That’s on top of the 200 already announced. And the news division is still nowhere near its target of £51m of cuts.

And with only two fifths of the £500m of total savings now announced, there is still a very long way to go.

As a BBC user, you are going to hear much more about cuts in the coming months. Some will think that is a good thing as the BBC reflects the belt-tightening going on in most homes and companies across the UK. Others fear that the BBC’s important role in public life is being chipped away.

There is a bigger fight going on here. The BBC is negotiating with the government over its future – and how it will be paid for. It won’t harm the negotiations if it can show the corporation is being streamlined and made more efficient.

As long as it can also demonstrate that audiences aren’t being left behind.