I'll be more specific about what I suspect the actual intentions are behind the online safety bill.
A few months back the UK charged five retired police officers with hate crimes because they had a private WhatsApp group in which the police found content racist[1] comments about the Duchess of Sussex (Meghan Markle).
In the UK it is illegal to say something online that could be considered hateful. But the issue is that in most cases when people are saying hateful things they do so in private, so most of the time offenders like these retired police offers go unpunished.
People in the UK are very concerned about hate speech, and unlike these surveillance stories, this is something that UK media obsessively report on.
The issue is that although the government can arrest your kids for saying hateful things in public[2][3] they cannot do this when they're being hateful in private. If we genuinely believe we need to stop hate speech, then it follows that we also need to do something about the large amount of hate speech which occurs in private.
I suspect this is the primary reason why the government wants to know what content you have on your device and what you're saying to your friends because it's likely some of it is hateful, and if you have said something hateful in private then they want to know.
[1] 100,000 people were charged with racist hate crimes last year, and around 1 in every 400 people are charge with some form of hate crime each year. I'm providing this context because these are extremely unlikely to be highly racist messages on par with what you might hear from say a neo-Nazi. More often than not it's simply something negative which could be classed as hateful.
[2] Police arrest autistic child for commenting that an officer looked like her lesbian nana, https://www.bbc.co.uk/news/uk-england-leeds-66462895
[3] 17 year old arrest for tweeting Olympic driver, "You let your dad down i hope you know that". It was deemed "malicious communications" because the divers dad died the year before, https://www.express.co.uk/news/uk/336534/Teenager-arrested-o...
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Legal note: I do not agree with hate speech in any form. My comment is not intended to downplay the seriousness of hate speech or question our need to enforce hate crimes, but simply to note that a lot of hate speech currently goes unpunished due to E2E encryption and the governments lack of visibility into what we do on our private devices.