I believe the Pharisees who called for the Crucifixion of Christ Jesus assumed responsibility not only for themselves but also for their children who would be responsible.
In a time which the individual man was immersed within his nation or clan or tribe the responsibility for acts accomplished by someone within the tribe fell upon the whole tribe. this is because the individual "Ego' hadn't been released as of yet and the individual correspondingly felt, experienced himself as a tribal member (I and Abraham are One). This was secondary to a natural causal relationship, not a relationship of intellectual choice. the individual identity of the individual man had not yet blossomed forth. Mankind did not fall to the earth running until after the event of Golgotha in which we finally became "Ego Beings" working the earth.
During our times tribal or national identity has on the whole not been held responsible for an invidious act but of course nationalism is the other side of the coin. The reparations of the Treaty of Versailles were onerous, by most accounts, but were directed against the nation of peoples even if those who wrote it disagree(read the Brits here).
Of course following the Second World War individuals were held responsible, Japanese and German. Condemnation of the entire peoples were withheld not because there may have been some who desired this but because in the movement of the individual as an "Ego Being" he sees himself and others in the same light. Democracy is one political manifestation of the development of the "Human Ego".
The term "on us and our children for 3-4 generations" was not unknown throughout the ancient world and it was a call for responsibility for a nation's or clan's or tribe's acts. The nation was responsible and if untoward manifestations of an act were brought forth the nation had to balance justice.
Considered in another light , being responsible as a nation (sons and daughters) for an invidious act is actually is actually liberating. but there is also the question of what does one do in order to right the wrongs of a nation but then I'm speaking as an individual and have not transported myself into the being of the nation of that time; the trials and tribulations of the Hebrew Nation would better answer that question but of this I am not able to say.
cliff notes: the ancient tribesmen were ensconced within their nations in a clairvoyant manner to which they could connect with their progenitors, not as individuals but as a living breathing part of the entire tribe. And so, their children would have their responsibility truncated after 75-100 years which is not a bad deal when the background is considered.
After all, if one could not "think or breathe individual" as we do today then where does the responsibility lie?