“how would one divine damages for e.g., copyright infringement from the Gemara?”
There is actually quite a bit of halachic literature on this. Communal authorities have at times granted exclusive licenses for some seforim. I’m not familiar with this topic, though; perhaps RSRH can enlighten us.
In any case, copyright infringement is a violation of secular law.
“I do not think correcting misconceptions among those who do care about Jewish law is an empty effort at all”
In addition, dina malchutcha dina IS halachah so it is important that dayanim understand secular law. Aspects of secular law such as taxes affect property cases in batei dinim even according to the most minimal interpretation of dina malchutcha dina. Finally, a beit din must be sure that its decisions are not inconsistent with mandatory provisions of secular law or the secular courts can overturn them. A dayan needs to know a lot of secular law.