I see your point and would be more sympathetic to it if we had proper sex education in k-12 and made birth control and abortions easier to obtain for poor people. Even so, clearly this lady made some poor choices.
Or you could simply put the kids into foster care. Which has a very bad track record compared to being with mom.
So the data leads to prevention. (Education, or forced sterilization/abortion.)
I also think calling the comment a 'trope' is unreasonable. This looks to be an incredible lucid example of possible, if not probable, abuse. Yet that's masked in the appeals to pathos. How is mentioning this anything like a trope? If there is viable reason to believe that empathy/sympathy is being abused, it certainly seems valid to consider it and point it out!