It's you who's wrongly associating it with paedophilia and drugs (both amply available on the 'clearnet') IMO, which does quite a disservice to attempts to promote Tor to the newly privacy-conscious.
'Dark' means hidden, not 'evil'.
> The Tor browser is privacy-focused software used to access the dark web
Yes it is. But that's the worst thing it's used for.
It's like saying 12-gauge shotguns are used for bank robberies...
Ok, I'm stretching the point but it's needlessly putting the association of privacy focused browsing using Tor with the nasty shit that some people do with it.
Edit: I realise my understanding of The Dark Web was incorrect so this argument is invalidated now but I'll leave it up.
The "dark" in dark web doesn't mean "bad", it's darkness to prying eyes. If you buy drugs on the dark web, it's the dark web. If you read literature on the dark web that your government doesn't want you to read, it's the dark web as well. The negative connotations you're associating with it are what this step by the BBC will help reduce: pointing out that the criminal use isn't the primary use of the dark web. Privacy is.
On that note, I bet if you asked non-techs what they think "dark web" means they'd think nasty stuff.
That will change when more normal stuff is available on the dark web and the privacy aspect gets more pronounced (privacy being a major topic these days). And "we're providing access to the free internet to everyone living in countries with authoritarian regimes that try to restrict information and oppress their citizens" is a powerful narrative. They'll be less likely to consider it evil if it's compared to the BBC German Service during WW2, broadcasting to Germany in German, unrestricted by the Nazi government.
"The dark web is the World Wide Web content that exists on darknets, overlay networks that use the Internet but require specific software, configurations, or authorization to access."
Sure, many so-called Hidden Services offer illegal and immoral content, but the dark web is enormous. There are many more such sites offering ebooks and other (legal) media, anonymous blogging/forums/social media, whistleblowing services, censorship-resilient news platforms (BBC, NYT, The Intercept, ProPublica), cryptocurrency trading, and so on.
Hell, even the CIA has a 'dark web' presence on Tor [1].
[1]: http://ciadotgov4sjwlzihbbgxnqg3xiyrg7so2r2o3lt5wz5ypk4sxyjs...
I would say to most people, if they have heard of the "dark web" then they think it exists exclusively for "the nasty shit".
I think I've seen the exact BBC article ;)