Answer

What is “the state”? There is no state treasury in the Talmud. Perhaps the king’s treasury (which also did not really exist, though in principle they do discuss it).
As a rule, penalties are paid to the injured party, not to any public treasury. It is true that with a penalty the goal is not compensation for the victim but punishment of the offender, so the main thing is that it comes out of him, and it does not really matter where it goes. But if he is already paying, then why shouldn’t he pay the person who was harmed? Usually, monetary compensation does not truly make up for the pain and anguish.
I remembered an article by my student, Rabbi Bezalel Daniel, in Meisharim 3 on this subject. Here it is:
https://asif.co.il/files_author/%D7%94%D7%A8%D7%91-%D7%91%D7%A6%D7%9C%D7%90%D7%9C-%D7%93%D7%A0%D7%99%D7%90%D7%9C/