When I was in university, I had Spanish 2 with a teacher who was bilingual and Spanish 3 with a foreign teacher who only spoke Spanish. If asked on a survey which I preferred, I would definitely say the bilingual teacher purely because it was less stressful to not have to communicate in Spanish all the time. But I learned MUCH much more in Spanish 3.
I'd say 90% of the Spanish I remember today was from the foreign teachers class. I remember tons and tons of things I learned, mostly from days when I was horribly embarrassed and desperately trying to figure out what he was asking me and how to respond to him. Oh God did I hate that class (I remember crying during it once out of frustration) but not using your native language is definitely the best way to learn.
I don't blame the kids one bit for saying they would rather have someone who speaks both Korean and English. It's much easier to breeze through and less embarrassing for them. But it's not going to help them learn anything in the long run. I know today many of the kids don't care about English except as a way to pass tests, but sooner or later they are going to run into a foreigner who will speak English to them, and only then will they realize that there aren't any multiple choice answers.
Fair enough comment and I'm sure there are plenty folk around with similar experiences who draw similar conclusions. However, I think you've got to keep in mind that what might work for young adults in a university language class isn't necessarily going to work in the same way for elementary, middle or even high school students, particularly when it's a language they didn't choose to learn and may even resent doing so.
As it happens, my own experience of native speaking teachers at the equivalent of middle and high school is pretty much the exact opposite. We had a German assistant for 2 terms and he was absolutely f-ing useless. Of course, he spoke perfect German but he couldn't teach to save his life and had utterly no idea how to relate to British kids. One class actually locked him in a store cupboard.

Looking back, the only thing I learnt from him was that being able to speak a language well, even as a native speaker, didn't necessarily mean you could teach it. His one asset - his native speaking ability - wasn't really any advantage because the 2 British teachers of German I had spoke the language to an excellent level anyway. Thanks to them, I achieved the highest grade possible in my A-level German (the public exam you take for uni entrance in England).
That particular native speaker helped me not one iota, however at least he didn't turn me off the language. Because the native speaker I had for French did just that. When I took the exams you take at age 16 in the UK, I was good at both French & German but much preferred French. I continued with both from 16-18 but my preference was completely reversed. It wasn't the only reason but the main one was the teachers I had, and particularly a native speaker from Belgium who taught us for 2 terms as a trainee teacher. She just about had more idea of how to teach than the German language assistant, but had likewise little idea of how to relate to the students she was teaching. Unfortunately, whereas our regular teachers for German were clued up enough to realise the limitations of the German assistant, the head of the French department had her head up her ass and thought that maximum exposure to a native speaker would, per se, by osmosis, make us all better at French. It didn't. Not in one single case of 10 in the class.
I'll stress again here that I'm
not concluding that native speakers in the classroom don't do any good. I'm sure that many times they do. But the idea that
just their native speaking ability is enough is a dangerously naive assumption IMO. Amongst other things, they'll need some ability to impart their language knowledge and to be deployed appropriately by the schools/educational authorities that employ them.