1) His rights are heavily dependent on cooperation from the kids' mother
Fathers are often illegally denied even court-mandated visitation. A father can't simply file a police complaint if he's denied visitation. He has to go through the court system and even then may not get compliance from his ex.
2) The level of mandated child support can be arbitrary
Judges have discretion to alter the amount and may not care what a father can actually afford in an economy where employment is often temporary or project-based. In Germany, a fictional income can be assigned to a father based on his educational level that may not bear any resemblance to the reality of his potential income and he may be told he has to take another job. In addition, if he lives with a new girlfriend, the amount of money he can keep for himself can in some cases be reduced to as little as $970 a month.
3) He may have to move away from where his kids live to find work or due to a lack of affordable housing
This is linked to #2, and may also mean the loss of a visa and therefore access to his kids. Being a long distance away from your children means you don't see them as often and makes even limited visitation more difficult due to transportation costs and an inability to bring kids into a shared living arrangement for a visit (or one that is too small). If you share an apartment with three other adult men, is that an ideal place to bring your kids for a visit?
4) Work schedules may also not align with the children's vacations.
This is especially true if he has to work two jobs or work overseas to be able to pay child support.
5) He may be falsely accused of abandoning his kids or not caring about them
We've recently seen this here on GAG, and it happens not infrequently. There is a tendency to ignore the father's perspective because the mother is considered to be the more vulnerable party after a breakup. This is not always true, especially in an era in which women often earn more than the father of their children even before child support is paid and have a better support system.
I can tell you for a fact that being away from your kids has a huge emotional effect on you and is not something most fathers want or don't care about.
Please try to bear in mind what I have explained here before you judge a father who isn't living right next door to his kids after a breakup.