Spoiler warning!
The children were being incorporated into the bodies of the aliens. In the words of the rather terse (and uber-creepy) alien ambassador:
They create chemicals. The chemicals ... are good. We feel ... good. The chemicals are good.
Basically, they were being used as prosthetic glands secreting a narcotic, which the aliens found pleasant. That's why they wanted them. The aliens were shooting up, children. Somehow the (original 1965) children were preserved in their adolescent state, presumably indefinitely, melded into the alien's monstrous bodies. The nature of their subjective experience was left undisclosed, but it is hard to imagine it was pleasant, nor that, being reduced to glands, that they had any sort of autonomy.
So yeah, being a cancer patient or otherwise unhealthy child did not appear to be any 'advantage', at least not from the perspective of the child, since presumably their suffering existence would only be extended forever. Hard to see how the parents would see this as a plus either.
Lesswrongers will be encouraged to learn that the Torchwood characters were rationalists to a man and woman - there was little hesitation in agreeing to the 456's demands.
Are you joking? They weren't rationalists, they were selfish. There is a distinction. They were looking after there own asses and those of their families (note that the complicit politicians specifically excluded their own family's children from selection, regardless of 'worth').
children - or units as they were plausibly referred to
What do you mean by 'plausibly'? They were referred to as units in order to dehumanize them. Because the people referring to the children as such recognized that what they were doing was abhorrently wrong, and so had to mask the fact, even to themselves, by obscuring the reality of what they were discussing: the wholesale slaughter of their fellows.
... governments paying attention to round up the orphans, the refugees and the unloved - for the unexpectedly rational reason of minimising the suffering of the survivors
That's laughable. It had nothing to do with minimizing suffering, that was a rationalization. They were doing it for the same reason any government targets the vulnerable; because there are few willing to protect them and argue for them. It was pretty clear if you watched the show that the children being targeted were hardly 'unloved'.
You can't consider the scenario without considering the precedent that it would set. The notion that there are wide swaths of the population -- children, who've never even had the opportunity to truly prove themselves or do much of anything -- who are completely without worth and sacrificeable at the whim of the government is untenable in a society that values things like individuality, personal autonomy, the pursuit of happiness and, well, human life! They would not be saving humanity, they would be mutilating it.
The poster failed to mention that the sacrificed children were being sentence to an eternal fate which worse than death.
And there is a difference between the actions of the government and the actions of the main character. One of them was fighting the monsters. The others were the monster's business partners.
I can think of a couple of differences:
The poor people during a famine at least have a fighting chance, if slim. Somehow, by hook or by crook, attain money or food, or leave for a region where there is no famine.
Also, a famine is a matter of public knowledge, which allows the possibility for a society to collectively (or fragmentedly) come up with a solution. In the torchwood scenario, [small spoiler warning] the true nature of the threat and the solution devised by the executive branch were being kept a secret. In fact, they were actively suppressing groups who were moving for alternative stances towards the alien threat. If it were public knowledge, the to-be-sacrificed class would at least have the option of revolting against the powers/system/'algorithm' which was mandating their extermination.