You're assuming that a family with 3+ kids has the time and energy to also keep 2 full-time jobs...even with flexible hours etc. It won't work.
We have 5 kids, so I know what I'm talking about...and my wife is working part-time, after being at home for 12 years.
If you want larger families, you need to help families have a spouse stay home...possibly for years. That means, for starters, stop taxing the wage earner essentially the same rates as a single person with zero dependents.
Show me 1,000 families with both spouses in the workforce, and I will show you 973 families with 2 kids or less.