Because the society considers such culture good (working at an old-style company is more approved of); established companies have government, business, and family ties that give them enough advantage to get away with some inefficiency; and people who don't believe in these values (i.e. potential founders of companies that would disrupt these values) are by definition so far outside of the mainstream that they may have trouble accessing social resources like capital and advice.

There are endless reasons why societies and economies converge on non-optimal ways of doing things. The market doesn't fix everything.

"There is a lot of ruin in a nation." — Adam Smith

This seems to be true of all sorts of large, complicated systems. Smith naturally focused on countries, but large organizations like companies and nonprofits can waste resources like this, too. The human body exhibits this behavior, too — imagine how many things that could go wrong with yours that would nevertheless still leave you able to go to work.

Well, there's more to a successful company than this. Simply being an established company can have benefits that outweigh this, perhaps very strongly so in Korean culture.

Part of it is capital. The chaebol completely dominate the Korean economy and any serious competitors are taken out with mergers and acquisitions. The other part is that the model works and the companies are profitable. Sure, they could be more profitable with less wasted time and more productive employees but they already have an overwhelming majority in the Korean economy and they are globally competitive. It irks me to see more productive methods of work that are not adopted but yo can see that in every country.