I don't think it's "simply" a disability insurance policy. Pregnancy can be planned. If someone were to buy an insurance policy before they conceived, pay $100/month for a year or so, then get 60% of their salary for 3 months (much more than they paid in probably), they'd just cancel the policy afterward. The insurance company would lose money on this every time.

Some quick googling suggests that there are disability insurance companies that will cover maternity leave, but they must be making a profit on it somehow or they wouldn't offer it. Besides which, I don't think there's any way paternity leave could be considered a disability, so it's no help there.

If this were rolled into social security, the cost could be more spread out. Since it's beneficial for us to have a growing population, I think it's in all our interest to support children being born, even if we don't want to have them ourselves.

It makes more sense to have benefits to employees focused on the employee side. It also makes it more fair (and more cost effective) if all benefits are equal for all; at least up to basic minimums that everyone should have for society to function well.