Today, I think the more common modern scenario is Alice voluntarily leaves Bob because she decides (perhaps rightly!) she could be happier elsewhere. In this situation, custody is often contested, but Bob usually ends up paying child support anyway. I think this is more often the sort of situation that leads people to question if there's a moral obligation to pay Alice when she's a single mom because she made the choice to be.
It is also important to note the while child support is the named purpose of the payment, in practical terms Bob is simply paying Alice and Alice treats the money as fungible and spends the money at her discretion; Bob may be (and usually is) directed to pay certain child-expenses separately and directly, such as daycare, school supplies, and health insurance. Child support is on top of these expenses and is usually assessed as a percentage of income; 15% is a common number. Generally, this number is much higher than the actual marginal cost of having a child living with you.
It is also important to note the while child support is the named purpose of the payment, in practical terms Bob is simply paying Alice and Alice treats the money as fungible and spends the money at her discretion; Bob may be (and usually is) directed to pay certain child-expenses separately and directly, such as daycare, school supplies, and health insurance. Child support is on top of these expenses and is usually assessed as a percentage of income; 15% is a common number. Generally, this number is much higher than the actual marginal cost of having a child living with you.