This is backwards. You're ignoring that the divorce has to be initiated in the first place and that divorce usually results in the removal of custody by the father and thereby creates an obligation to pay child support on the side of the father. Therefore divorce is causal. A desire to not pay child support does not lead to a child having to give up after school sports in the absence of divorce.
So let's replace what you said with reality:
>Think of the reverse perspective - is it fair for a child to have to, for example, give up after school sports, because their parents divorced? Or be forced to change schools and lose their social group because tuition is unaffordable on a single income?
Yes it is fair, because the divorce was initiated despite the expectation of these outcomes. If a man or woman initiates divorce, they must have had a good reason to do so and we should not question that reason by arguing that school sports or tuition are more important than the reason for divorce.