I wondering about that....
Yeah, it happens a lot more than we think.
How do I know? Because I personally know a
idiot guy who seeded up a Dominican in Santiago, DR a few years ago. She was pressuring him for child support AND "papers" (her words). She thought that she would get a visa or citizenship or something out of it. After he consulted with a few lawyers he found out that only his son can get citizenship and the mother does not get any immigration benefits unless he marries her. That's how I first learned about it.
It still is not automatic though. The father would have to file for the child to be a US citizen. The foreign baby mama can't do it on her own.
I think it is happening more now than ever before. With international dating websites, hookup apps, translation messaging (WhatsApp), and the passport bro movement...I think American dudes are planting seeds recklessly. Then ghosting when they find out the girl is pregnant.