I don't think there is a single manhwa I've read (except for fantasy) that doesn't mention the Jjang.

There's a Jjang in every manhwa and all of them have these gang fights with rival Jjangs. Each Jjang is usually so fearsome that underlings and fodder run away at the mere mention of the name of a rival Jjang.

90% of the time in shoujo manhwa, the Jjang is a Bishounen (or King Kah in Korean) and the main love interest for the heroine. Usually, a number of Jjangs fight over the heroine.

The Jjang can single handily defeat 20 underlings. The Jjang is also usually very rich.

Is being a Jjang such a prestigious position in Korea?

I think the Japanese equivalent is the Banchou. However, Banchous are relatively rare in manga and anime and the ones that do exist are usually big muscled manly men.

That's what happens when you read shoujo. 90% of them use the same plot devices and outlines.
I could mention a few shounen/seinen manwha in a school setting without a Jjang in it, let alone one that is somehow a pretty boy who, dispite his girlish face and build, still seems to be able to give a good punch.
But the only thing in those cases would be trading in generic shoujo plots and stories for shounen ones.

________________
Do but despise reason and science,
The highest of all human gifts -
Then you have surrendered to the Devil
And must surely perish. - J.W. von Goethe

It doesn't even stop there. About 90% of the K-dramas and movies I've seen include delinquents and gangsters in some form or another even if the main story has nothing to do with it. Either Korea is overflowing with outlaws or like you said, being a gangster is cool and something to aspire to. Rather sad...

yeah, remind me never to read Shoujo manhwa...

Um, neither. The U.S. has a ton of CSI series and whatnot but is every neighborhood replete with it and we aspire to be either the murderers or the investigators? etc. (Obviously, I'm just using that as an example.)

Ditto.
Try other genres.