I 100% agree that the cost / benefit analysis in this scenario is clear-cut.
However, it's also the case that "experts" are occasinally completely in left field, and when challenged by non-experts, have exactly the same "You're not equipped to make this decision" attitude. Doctors who prescribe drug after drug to elderly people, until they have functional dementia due to drugs and nothing to do with any underlying health issue.
And the same thing can happen for entire fields, when one strong-minded "expert" manages to make one particular way of doing things or looking at things the "orthodox" way, and the field as a whole rejects any doubters as heretics. (There was recently an article on HN about how most educational researchers think whole-word reading is a terrible way of learning, but how most educators think that's the best way.)
Diversification of decisions is one of the best defenses we have against that.
Or to put it differently: There is a risk if we allow parents to make this sort of decision on behalf of their kids: that a number of parents will be fooled by charlatans into making decisions that harm their kids. But there's also a risk of not allowing parents to make this sort of decision on behalf of their kids: That a single well-placed wrong individual can make a decision which harms untold millions of children.
There is certainly a time and a place for overriding parent's decisions about their children; but it should be made in circumstances where the costs of doing so are crystal clear.