I need some input, please!

I’ve been a single mom since day one. My son’s father didn’t want to be involved in our lives. I never considered filing for child support until my son turned two years old. When I did file, BD reached out to convince me to withdraw it, which I refused to do. When my son was three and a half years old, he began expressing a desire to see his dad, so I contacted BD. He agreed to video calls (we live 2,000 miles apart) and even flew to our state to meet his son for the first time. After that visit, he continued to try to persuade me to cancel the child support and I refused, so he stopped calling. Months went by, and my son was feeling hurt by the lack of contact with his dad. I eventually agreed to ask to close the child support case, but only if BD maintained contact with my son. They didn’t close the case because BD owes back payments, although I didn’t mention that to him. We only got two checks for $14 each. They reconnected and started having calls again, and they met in December. He learned the case was still open. So the calls have been inconsistent. He calls on Saturdays. I know he is only doing this to get me to cancel the child support. He doesn’t seem to genuinely care about my son, and I am allowing all of this for my child’s sake because he gets so happy when he talks to his dad. My father died when I was my son’s age, so I know what it feels like to not have a father. Should I go ahead and ask the court to close the child support case? If the father decides to stop contact after that, should I just let it go, considering we haven’t received any financial support anyway?