Children inherently cost money. Someone has to pay it. You're trying to pretend like the system is designed to screw parents by burdening them with this cost source that is a child when simply put, children cost money.
> How many people do you know that had to keep working to put their kids through college?
College costs money. The incentives with government backed student debt has inflated that cost dramatically. This wasn't some scheme to tax parents. It was a moral hazard of a bad policy intended to make college accessible but in turn caused massive tuition inflation.
> Why does it cost employees to add children to employer-sponsored health insurance?
Again, because insuring more people costs more money. Whether you're adding a child or a spouse, more insurance coverage ought to equate to higher premiums. That the economics of how insurance works. Again if there are higher costs, someone has to pay them.
> The system is very much set up to disincentive having kids.
The system does disincentive having kids but that doesn't at all imply the system was intentionally designed to do so. (A) kids cost money and that is by definition a disincentive and (B) some policies like college loans were not setup to cause this disincentive. They instead just had adverse effects due to the moral hazard of incentivizing colleges to raise tuition since the government will back the loan and the student doesn't understand how to make an informed decision on cost tradeoffs at their age. But this isn't the system being designed to prevent people from having children.