Because I don't want to live in Korea for 2 years. Flying isn't the reason for not going to Korea.
Does the military even allow the family to live in S Korea? I know at one time they did not.
I'm coming up on the end of my year and a half in Korea (we got stuck in the change of the program, otherwise it would have been two years) and even in the time I've been here I've seen things improve quite a bit. It really isn't that bad. I know it's a personal choice, but coming over here isn't an experience I would change, even though it means I haven't been to Disney in almost 2 years.
Also, the money is really good over here. I've been able to afford going back to the States twice for dying grandparents and we still have managed to save quite a bit more on top of that. Pretty much everyone I know here manages to save quite a bit of money whether they come with sponsorship or without.
My biggest regret is that we didn't get to go to Tokyo Disney while we were her, but that's because I decided to go back to the States twice for dying grandparents.
If two years is too much for you, it is possible to come over non-command sponsored and just do the year tour. I don't know that I'd be willing to do that with kids (especially older ones) but the entitlements are pretty much the same, except you have to pay for your plane tickets (being at Fort Lewis gives you the easy option of SpaceA on the Patriot Express) passports (which I recommend everyone having anyways) you don't qualify for DLA or CSP pay, and your weight limit is lower.
There are Facebook pages for all the different installments over here (Camp Casey, Yongsan, Red Cloud, Humphreys, Osan). It might be worth it to check them out.
When I first started researching Korea I was really turned off by it as well, because of the lack of information available to me, but now I know where to look.