It's less than "only the poor people want to reproduce" and more than "people wanna reproduce" and "so many people are becoming poor these days".
The middle class is GONE, and the lower class has grown immensely. So as a proportion, sure, they reproduce more. But that's just because we've grown so many of them.
This isn't entirely accurate. The shrinking of the middle class is accounted for entirely by movement into the upper-middle (and higher) income classes, and what you say about the lower class ignores per capita data.
The middle class is GONE, and the lower class has grown immensely. So as a proportion, sure, they reproduce more. But that's just because we've grown so many of them.