This is just my opinion:
Jeju happens to be, based on potential, I think, one of the most beautiful places in the world. "Potential" is the key word. In reality, I can't wait to get back to pure nature in the secluded mountains of the Blue Ridge, and am counting down the days.
Back to Jeju. There are two things (and an additional minor note), that Jeju could do in the future to live up to its slogan image of "The World Comes to Jeju, and Jeju Goes to the World." For the world (outside of Chinese, Japanese, and mainland Koreans) to come to Jeju, there have to be reasons. And, tourism may be the only thing Jeju has in the future.
The island has three main environmental positives: UNESCO sites of Hallasan, Seongsan Ilchulbong, and the Geomunoreum Lava Tube System, many diverse beaches, and the ever popular Olle courses. The main problem is these are not environmentally pristine. They're dirty. However, this can be solved.
Jeju's beaches are definitely worth visiting. Each one offers something another doesn't. But, for world travelers to come and spend money, the beaches need to be clean and pristine. It can't be that hard for the government to invest money in infrastructure and equipment to make this a reality. Industrial sand sifters exist! And I've worked on smaller ones with an ATV having a pull-behind attachment 13 years ago out of high school working for my hometown's Department of Public Works at my local beach. This is not new technology. Having garbage cans at every beach, that are artistic and ergonomically fitting to the landscape are a must. It is possible to keep the beaches clean and year round! True there is going to be garbage washing up on the beach daily. It needs to be picked up every day before it becomes a part of the sand. Jeju could have a real slogan it could be proud to tout to the international (outside of the Asian region) audience, something like "Diverse and pristine, Jeju offers 30 of the world's best beaches." Word of mouth spreads fast.
Olle courses are fast becoming trendy. But pure nature outside of Korea doesn't have thousands of empty plastic bottles and plastic shards to offer reflective hikers. It would probably take thousands of people a long time to adequately clean the Olle trails to a level of international standards, where some day a European is going to tell their friends, "I spent one week hiking Jeju's Olle trails and I didn't see one piece of litter. The nature was incredible." Now that is a pipe dream. Too many people in a small space. Keeping the Olle courses clean is the biggest problem. Subtle, yet well thought out and placed refuse containers, are again, a must. I am fascinated how collectively prideful Korean people are, but, collectively, not about their own environment. The Olle courses may have to move toward some classier markers, as well.
The pit toilets at the UNESCO sites must go. You cannot ask a fat European man or a high-class debutante to honestly squat at a UNESCO site. If international tourists are what the island desires, international toilets (at least throne, pit toilets) are what it needs to provide. It's as simple as that. Also, there are enough horses on the island, calcium lime or its equivalent has to exist here. Have a worker spread it down at least once a week, preferably more. The UNESCO sites need to be clean. I've doubled over a few of the 100 or so times I have entered a pit toilet on Hallasan's hiking trails from stench.
I find oftentimes Jeju is like an American teenager. It has no identity. It's debating its next henna tattoo, or piercing, or sultry piece of clothing, yet with no thought to the future, just instant gratification. I've heard the cruel moniker "peasants with technology" label from international travelers. Rise up Jeju people. Take more pride in your land. Travel. Realize that Korea is less than 1 percent of the world's population and it may be shocking the other 99 percent may think a lot differently than you have been taught. Travel will reciprocally also offer an opportunity on how to improve the future of this island's tourism.
International tourists will come if there are reasons. Find ways to make this happen, instead of saying they are already here.