The gemara asks why the Mishna needs to tell us that we read the first parsha of eigel harishon with the targum – why would we think not? Answers the gemara: the whole episode is an embarrassment to Klal Yisrael, and therefore, one might have thought it better to pass over it with no further explanation or embellishment. Kah mashma lan that precisely because it is embarrassing it is read, as those involved want to suffer that bit of embarrassment so that they can get a kapparah.
The Meshech Chochma makes the clever point that our not extending the same reasoning to the parsha of eigel hasheni, to Aharon’s explanation of what he had done, proves that Aharon was granted a complete kapparah without needing the added embarrassment.
Be that as it may, I want to focus on a little comment of R’ Ya’akov Emden. The Yavet”z writes that we see from this gemara that even the dead are capable of achieving kapparah. Those who worshipped the eigel are no longer with us, but still, apparently they suffer embarrassment at having their misdeeds recounted and through that can achieve forgiveness. (The Rama similarly writes that the reason we say yizkor on Yom Kippur is because it is a day of kapprah for the dead as well as the living.)
Is this really a proof? My son’s rebbe in another context has said over a mashal from the Sh"lah: someone being prosecuted for a crime cannot say in his/her defense that the culprit was a bunch of other molecules, but since then their body has produced new skin, new blood cells, etc. and they are now a different person. The meforshim ask how the oath administered in Parshas Nitzavim as part of the bris between Hashem and Klal Yisrael is binding on future generations – those generations haven’t been born yet and haven’t given their consent? The answer is that when we speak of Klal Yisrael, those future generations are like new blood cells, new skin cells, etc. – the identity of Klal Yisrael remains constant, even if the parts undergo change. Here too, the way I understood the gemara is that the kapparah for the cheit ha’eigel is not something being given to the dor ha’midbar, who are long gone, but is being given to us, something we need, because we carry on their identity.