Thats quite the leap of judgement, and I'd say its almost certainly not true (and quite possibly the opposite, I know thats been the case for me).
I could achieve before some tasks in 3 mins by just going to respective folks, interrupting them nicely and get the stuff done. Now I am chasing them for a week for same trivial task.
May not be an issue at Google, I would expect them to be less dysfunctional then our broken corp, but most multinationals are super far from well oiled machine.
As for my current position, its certainly not Google, and I wouldn't call it a well oiled machine. Don't get me wrong, its a really nice place to work, but yeh, we have a few of our own problems ;)
Anecdotally, I have small children at home and worked from home even before the pandemic when my company had an office. I have climbed the corporate leader every evaluation period because of my performance, while coworkers who were exclusively in the office weren't so fortunate.
It just goes to show that people are very different and it's impossible to generalize statements based on a single variable (has_children=True)
Are you responsible for your children? If not, then with regards to work(load) its akin to having no children at all.
You say its arguably false, yet ~90% in my team have children (I'm one of the few with toddlers). And the one who doesn't have children split up recently (due to relationship stress, which now lead to more stress, the irony..). Everyone in my team's productivity suffers since they have to work from home.
And on top of that, there's another data point: mothers. They get structurally paid less than men and other women.
I guess I have the habit of keeping my work documented which helps when I'm asked for proof of anything. But at the same time people can see how much work I do at any time too.
Of course personal experience is far from hard data, but with a lack of decent data to go off on the subject (partially to do with the fact that productivity is a very vague term, with many disagreeing on how it should be measured, especially with the constant number of external factors affecting it), I can only go by what I experience. I also notice those with children think they're being less productive, whereas the rest of the team doesn't actually notice, so that could be a factor.
Thats not saying that WFH is beneficial to all, of course not. I think theres a massive range of factors, children of course being one of them, but I think it comes down to the individual, rather than any broad strokes we can attempt to make.