What does that even mean? The only cases I can think of are: an ad loaded from a site which is not blocked, and a legit typo. (like ripe.com was a porn site in the past, when I meant ripe.net) But "vast majority" sounds really unlikely...
Porn sites are blocked as you'd expect. It's rare to end up on one of those unintentionally, barring typos / odd results in search. But...
archive.org is blocked. VPN companies were blocked until very recently - but not VPN endpoints. Image hosting sites are blocked on a coin flip - deviantart is blocked, imgur fine - both seem to have a similar level of adult content, the rest seem to be 50:50. Reddit, including any and all 18+ subreddits, and reddit image hosting are fine... So it goes on. It just discredits the whole process.
I bump into it far more often than I'd ever have predicted, and get annoyed by it regularly - yet I have never once, in a decade of mobile net use, tried to get knowingly to pornhub or whatever. Mobile phones are too small for porn. :)
Given how many people have let their kids drain their bank account by letting them play on their phone, I disagree.
and,
the children's ability to access porn through their parent's mobile phone over a phone network,
are unrelated?
That doesn't seem the case to me. In my experience, even very innocent searches can (unfortunately, and unexpectedly) bring up porn-related material.
Regardless of view on whether "for the children" blocking of porn is good or bad, everyone doing so seems to have proven utterly hopeless at it. Hopeless for those who prefer to see it, and those who prefer not to. It's inept all around.
An example I read the other day was of a woman who had a new phone account locked down for 'adult content' as per new rules. She was complaining that it was flagging things like mumsnet as adult content.