The tax benefit for having a child only kicks in after you choose to have a child - the process of having a child also would take money, and the decision to have a child implies savings for the child, which costs money
Marriage helps with child rearing in a few ways - it helps in reducing the need for paternity tests, ideally providing multiple incomes to support the child (Whether through a marriage, or through a child support alimony post-divorce, either way works out to some extent), and helps with determining family names for an ancestral record of who is related to whom.
But there's a problem with only providing tax refund on having a child - there's costs incurred to have a child (Some of which mostly apply to having a planned child more than an unplanned one, but nonetheless, still exist as a cost):
1.) They need the free time to engage in the act of sexual reproduction;
2.) They're going to incur multiple costs of pregnancy tests, and the follow-up appointments that come from needing an ultrasound/additional healthcare;
3.) The amount of food they're going to eat during the 9 months pregnancy period will likely increase;
4.) They'll want additional things to have at their home when the child is born;
5.) Any miscarriages or unplanned abortions that happen would effectively make all the above for nothing, and would require trying again and incurring all the costs again (If they really want that tax benefit, or if they just want a child for non-tax benefit reasons.);
6.) If they do in fact have the child, now they have maternity and paternity leave often being used to care for the newborn baby, and there are additional costs involved.
Most married couples that plan to have children will, if they aren't able to save up to prepare for those costs, simply not have a child (Or perhaps they'll just adopt or foster a child - but that's not the usual reason for a tax benefit for children.). Tax benefits of simply being married, however, would allow married couples that plan to have children save up more as a result of the tax benefit of being married.