It's not that long ago - maybe half a dozen generations, when people got married and had kids very young - 15 was not at all unusual, unless they were 'high society' and marriages were as much about inheritance, joining family estates and so on. We're talking even mid-19th century here. Some of your great-grandparents might even have got married at 15 or 16 - my great great grandmother was already married at 17.
People's life spans were shorter, so they had to get started earlier. People were poorer so they couldn't hang around at home until they decided to get married, they had to get out and start a nest of their own. They didn't spend quarter of a century or more - almost a third of their lives - in education, or expect to put off having children until into their late thirties / early forties. People also had kids young so there would be someone to look after the parents when the parents got too old - no social security net back then. The family was less nuclear - poorer people especially often lived several crowded into a single room. While this may have been uncomfortable and crowded it also meant there was large extended family to help with the rearing of the kids. Grandparents had their role to play - babysitting while parents worked, and not shoved into a home or a 'granny flat' of their own to while away their last years. There was hiher infant and maternal mortality mainly due to poor medical care and hygiene awareness, though midwives were usually very good at their jobs.
In short there's nothing impossible about teenagers having healthy babies, and raising them perfectly well in a loving family with grandparents helping out as they have done for generations. We've done it for most of our evolution up to the last 100 years when changes in fashion and society have made it frowned upon. As for paying social welfare to support such people - while I would hope they'd be honest and look for a job as soon as they can, I have no problem with my taxes going to them so they can finish school, try and get a job etc.,
With our very low birthrates in the West we should be applauding anyone who manages to bring new kids into the world. In France the government actually gives parents a bonus for every extra child. Kids who are born into wealthy families don't necessarily get any more love than those born into poor families - wealthy parents might also feel able to 'compensate' for lack of attention with money, cars clothes etc., hardly ideal parenting either.
I've had to simplify and generalize a bit here to cover such broad sociological issues but in short the kind of society we have today when people stay at school until they're 23 or more and get married in late 20s early 30s and have kids same time is an aberration in the sense that's not been the way it has been for most of history. maybe our bodies and instincts haven't caught up with the 21st century western lifestyle.