You keep insisting this is the motivation for proposing sterilisation as if the rest of us are just far too emotional to objectively consider ways of guaranteeing this young woman can never inflict harm on another child. It's not about calculating risk it's about eliminating it
You can't for a single moment pretend that sterilising this woman would guarantee she can never inflict harm on another child, when the world is teeming with children, and still will be after she is released from prison. Prevent her having any more children of her own, of course, but do you honestly think removing her ability to reproduce somehow protects every other child on the planet, should she wish to harm one?
Beyond the ethical arguments around State enforced sterilisation, you also have practical and legal considerations. Lets say, for a moment, that you convince the government to act to change the law, what happens when this is immediately challenged as a breach of human rights? Do you honestly expect that lawmakers would happily wave this through the courts? Even if it does become law, which doctor is seriously going to participate in the sterilisation of an otherwise healthy woman for no good or worthwhile medical reason? Indeed, which doctor could participate without violating everything that underpins ethical practice?
I am not unilaterally against sterilisation in every single circumstance. It has it's purpose in cases whereby there is a risk of pregnancy in an individual with extremely limited capacity, but that is ethical in the sense that it is very clearly for the good of the individual. In cases of male sex offenders, there are some countries which offer voluntary chemical castration, which, while outcomes are still indeterminate, might actually be a reasonable route to reducing offending, even if it is only by a miniscule amount.
So I could, in theory, see a scenario whereby people who have committed crimes against children are offered voluntary sterilisation as part of the rehabilitative process, but how on earth you go about that without rendering the 'voluntary' part moot and essentially brow-beating people into having it done against their will I do not know. It already happens with 'voluntary' self-admissions under mental health provision, so I would still have grave doubts about sterilisation being practiced even on a 'voluntary' basis. There's no way in a supposed 'civilised' society it should ever be enforced involuntarily by the state on otherwise healthy people.
Slippery slopes are usually a pathetic Strawman, but in the case of eugenics, it really doesn't take much to go from 'sterilise criminals' to 'sterilise potential criminals'. It's not as if there aren't historical precedents, and given the bunch of populist right-wing clowns governing the UK, I really wouldn't put anything past them that they think might pander to a certain demographic.