Whether accidentally or deliberately pregnant at 16, it is frowned upon by society. So the idea of being 'rewarded' for such disgraceful and deviant behaviour forms part of the moral framing of who is worthy of welfare services and who isn't.
As others have pointed out there are different issues and ways of framing this debate that are not being clearly distinguished from each other. The argument around what all people should be entitled to regardless, the moral argument of who deserves such entitlement and what should happen to those who abuse the system or don't take responsibility for themselves, and then the issue of what is going to cost the state less?
A young single mother in a secure and safe flat is cheaper than a young single mother in a hostel or B&B without adequate facilities or access to healthcare and education for her and her child. But if we want to punish her for her behaviour and abuse of the system, then let her and her child suffer for it. As if it will make any difference to her so-called moral fibre... Ad astra per aspera
Can we imagine a society which didn't punish anyone? in which anyone's child was everyone's child, and there was no such thing as "illegitimate" or "undocumented"?
But then we'd have to imagine a society without patriarchy (without men's obsessive need to control female sexual and reproductive behaviour to ensure that "their" women only bear "their" children) and without nationalism (the obsessive need to control which people are allowed to live inside which imaginary lines drawn on inaccurate and irrelevant maps). Huge steps.
Is there any relationship between draconian cultural norm-enforcement and resource scarcity?
And yet, what of the overwhelming evidence that suggests there is more charity and reciprocal-altruistic sharing among people living in relative resource poverty than in relative abundance... that is, until a certain level of bankruptcy, or the "Ik threshold" at which humane behaviour disappears entirely and survival is an individual obsession (we revert from pack animals to solitary scroungers)...
head hurts. must get out in fresh air... The difference between theory and practise in practise ...