I'd say in our time, in 99% of situations: NOOOOOOO, but '14-sai No Haha' shows that 1% exception:

A wealthy society with the best medical service, decent laws, and many more favourable conditions, but let me say some words about the most important factor: The Family of this Teenage Mother!

A man and a woman marry & live with love, so they could bring up their kids as best as one wants. This means, even at 14, 'Miki' (Mirai Shida❤️) is full of love, confidence and power. She begins a romantic relationship with a nice 15-year-old guy. Due to inexperience, her first and the best possible experience of sex leads to pregnancy, but soon she grows strong motherly feelings that make abortion out of the question. It's true that she can't be a normal junior high-schooler anymore, but her family & society are ready to support her and she can have everything necessary at her own pace. Because of her age, I don't think 'Miki' is able to be a full-time mother, but she's totally capable of being a good part-time mother. As her family and others do the rest, there shouldn't be a real problem. Overall, both 'Miki' & the baby, 'Sora', will be fine, I think.

More generally and even in normal cases, I think it's a good idea if parenthood is shared by more and more people. It's too much for one or two persons!

There are many things about the drama that I don't like, like that journalist story. I'm also not a big fan of its over-dramatization approach, but I think the main theme is elaborated well enough that I can recommend the drama to people who like this topic of teen pregnancy.