Of course it's a disingenuous framing. A certain kind of person is both attracted to power and deathly afraid of people voicing unapproved opinions "outside their kitchens".
Things can have multiple justifications, some public, some not: some conscious, some not. Central control and a feeling that a parental figure is in control of the tribe primes, at a primal level, a certain kind of person to like an idea. The specific post-hoc justification is almost incidental.
That said, such things need a semblance of legitimacy to work. It'd be much harder to crack down on general purpose computing under the guise of safety if we had cultural antibodies agains safetyism in general.
I think the phenomenon is most visible in the United Kingdom. Not just with respect to the recent age verification measures, but also with respect to the government's recent financial misadventures.
It appears to transfer the guilt of a successful deception that manufactures consent to public morality and the vulnerable. The real issue is it couldn't succeed without mendacious officials that suffer no consequences and uncritical/supportive media pushing the ball across the line.
It's also a much broader phenomenon than "protect the vulnerable". There are many other overused buttons they press to seek consent e.g. fear being the most common. Fear of terrorism, fear of job losses or tax rises, prejudice of others etc.