"This seems related to the political question of how much healthcare costs should be socialized, i.e. spread across a group rather than shouldered by individuals"
But that story isn't about costs of healthcare - the NHS will treat her for free precisely because the costs are socialised. The social care system will also ramp up rapidly given she's a vulnerable new mother who has now been admitted to the local maternity hospital.
It's a moral question, not a political one. Food for thought: "Rough sleeper gives birth to twins outside wealthiest Cambridge college" - https://www.theguardian.com/society/2019/dec/26/rough-sleepe...