That is an interesting point, and not obvious why it would be so. In fact, it kind of calls into question whether the whole relationship is causal. The people who were able to WFH longer were more often in high-income jobs (service workers never got to do it in the first place, it was almost entirely an office worker thing). They were thus more likely to be in an economic position where they felt comfortable having another child.
This would also explain why it impacted the intensive margin (children per mother) but not the extensive margin (percent women who are mothers).
I don't have a problem with WFH where it makes sense, and I do think many societies need to look at how to help young adults become parents, but I am a bit skeptical of this particular relation. If you've ever been a parent with a young child at home, your estimate of how much work you could do would be possible is a lot more modest.