Part of the problem they're trying to solve is the outsized role the electronics division is playing in the conglomerate. The entire company is worth something like half a trillion dollars (about twice Apple), but something like half of that is the electronics component alone (my numbers might be a bit off, but the order of magnitude should be about right).

Because of the interlocking structure of Korean conglomerates, ill performing companies in the conglomerate can stay propped up by the others, creating a drag on the successful parts, while simultaneously making it harder to figure out which parts are doing well and which are not.

There's other issues to, like family ownership being deeply tied into the conglomerate (which should be publicly traded). This has created a "royal" class of citizens who have a very outsized influence in society even if all they've done was to be born and have their parents put them in charge of a small holding company to learn the ropes. The influence peddling scandal in Korea is also revealing how deeply intertwined and corrupt the relationship between the government, these families and these companies are, and the net result is that citizen investors (stock holders) aren't getting the maximum benefit they could from a more transparent and accountable corporate structure.

Samsung in particular has a huge role in the Korean economy, accounting for something like 10% of the national GDP.