The theory of reward

After all, rewards and punishments are given in response to actions taken freely. It does not seem logical to punish a person simply because his parents sinned when he did nothing wrong. Nevertheless, there are cases where God punishes a person by causing his descendants to suffer.

Give examples and we can discuss.

“Fathers have eaten unripe fruit, and six sons have become deaf”

https://he.m.wikipedia.org/wiki/%D7%90%D7%91%D7%95%D7%AA_%D7%90%D7%9B%D7%9C%D7%95_%D7%91%D7%95%D7%A1%D7%A8_%D7%95%D7%A9%D7%99%D7%A0%D7%99_%D7%91%D7%A0%D7%99%D7%9D_%D7%AA%D7%A7%D7%94%D7%99%D7%A0%D7%94

In those days they will no longer say, "The fathers have eaten a bad day, and the children's teeth will be set on edge." For if a man is in his iniquity, all the people who have eaten a bad day will have their teeth set on edge.

See also the entire chapter 18 of Ezekiel.

What about the fact that David and Bathsheba's son died?

The death of a child is a punishment for them and not for him. But it is described there that the child has also suffered for a week. Indeed, it is true, especially in light of the sources above that children are not punished for the sins of their parents (the law of bastardy is also harsh here).
Perhaps there was a special need for such a punishment for the parents, even if it is at the expense of the child. It is like punishing a sinful person with death and his family suffers from it. Or simply suffering that comes to a person without having sinned because there is some need for it. And it is true.

So in conclusion, isn't retribution for generations something that exists?

In my understanding, it should not exist, and the verses also say no. In practice, there may be situations where this is done if there are good reasons for it (i.e. goals that cannot be achieved otherwise).

I understand. Thank you very much!