The Gemara on amud aleph describes a series of historical situations that explain the function and choice of particular coinage or sum used in the half shekel contribution, that are reminiscent of the sin of the Golden Calf, not waiting for Moshe to descend from Mount Sinai, and the plot against Yosef.  One of the age-old questions is what function of justice is it for descendants,  hundred generations later to still suffer from and pay for the sins of their ancestors.

The Rambam in his Guide for the Perplexed (III:46) explains: 

Our Sages, however, explained the fact that goats were always the sin-offerings of the congregation, as an allusion to the sin of the whole congregation of Israel: for in the account of the selling of the pious Joseph we read, "And they killed a kid of the goats" (Gen. 37:31). 

Do not consider this as a weak argument; for it is the object of all these ceremonies to impress on the mind of every sinner and transgressor the necessity of continually remembering and mentioning his sins. Thus the Psalmist says, "And my sin is ever before me" (Ps. 51:3). 

The above-mentioned sin-offerings further show us that when we commit a sin, we, our children, and the children of our children, require atonement for that sin by some kind of service analogous to the sin committed. If a person has sinned in respect to property he must liberally spend his property in the service of God; if he indulged in sinful bodily enjoyments he must weary his body and trouble it by a service of privation and fasting, and rising early before daybreak. If he went astray in respect to his moral conduct he must oppose his failings by keeping to the opposite extreme, as we have pointed out in Mishneh-torah Hilkos De‘os (chap. ii.)...

The same we notice in the case of Aaron. He had his share in the sin of the golden calf, and therefore a bullock and a calf were brought by him and his successors as an offering. Similarly, the sin connected with a kid of goats was atoned for by a kid of goats. 

When this theory has been well established in the minds of the people, they must certainly be led by it to consider disobedience to G-d as a disgraceful thing. Everyone will then be careful that he should not sin, and require a protracted and burdensome atonement; he will be afraid he might not be able to complete it, and will therefore altogether abstain from sinning, and avoid it. This object [of the laws under discussion] is very clear, and note it likewise.

What the Rambam seems to be saying is that atonement, especially generational atonement, is a process and not just a mere act of punishment or retribution.  To change the consciousness of a people, a lasting impression needs to be made that eventually burrows deep into the very culture of the nation.  This is not something that can be quickly microwaved; rather it requires a slow cooking process.  Imagine if the 2nd or third generation of Germans said, “I think we atoned enough for the sins of our fathers.”  The moment they say that, is the moment they are vulnerable to destroying themselves again through the corrupt propensities that have not been fully eradicated from their collective national soul.