Why does South Korea spend so much money on R&D?
They don't. Anything as a percentage of GDP often isn't very meaningful. Countries with smaller GDP will appear to be spending "more" on just about everything because the denominator of the fraction is much smaller. (This is not to say that all of the percentages are larger, but that the percentages mask the small amounts in absolute monetary units.)
How much a "country" spends depends on how each relevant group allocates its budget. If South Korea happens to have a greater share of businesses that allocate more to R&D, the overall spending as a percentage of GDP will appear to be higher than countries with a greater share of businesses that allocate less to R&D.
The GDP of South Korea is worth about 1.7T USD, while the GDP of the US is 25.46T USD. The "huge" 4.93% that South Korea spends on R&D is worth 83.8B USD, while the "tiny" 2.711% on R&D spent in the US is worth over 8.5x as much, 717.3B USD.
Some sectors require more spending on R&D, while others require no R&D at all. According to South Korea GDP by Sector, about 29% of South Korea's GDP is in manufacturing. Meanwhile, the United States has only 11% in manufacturing, but 33.3% allocated to finance, insurance, real estate, and services. If R&D spending is adjusted for the size of the manufacturing industry, where the bulk of R&D spending is most likely occurring, South Korea has an adjusted R&D expenditure of 17%, while the US has an adjusted figure of 24.6%. While this could use refinement and is not a standard metric, it does indicate that South Korea could be under spending on R&D.
Some sources break GDP down into agriculture, industry, services. South Korea has 58.3% in services, while the United states has 80% in services. Using these values for adjustment, South Korea has an adjusted R&D spending rate of 11.8%, while the US adjusted rate is 13.55%. Although the disparity isn't as great, South Korean R&D spending is still shown lagging. South Korea's increased spending rates on R&D could be a correction for under spending.
Since the US is a much larger country, there is much greater variance across its territories. The NSF has State Indicators with a map of R&D as a Percentage of GDP for 2019. A few states spend a much greater share of their GPD on R&D than others. California is on the high side with 6.33% (227.9B), while New York is on the low side with 1.62% (33.2B). According to the Bureau of Economic Analysis, in 2022, the GDP of California was 3.6T USD, more than double that of South Korea. The GDP of New York was 2.05T USD. Manufacturing in California is 11.78%, close to the US average. Manufacturing in New York is 4.08%.
Now for fun, consider R&D spending from a few companies for the four quarters ending Mar 2023.
- Apple is a US company reputed to be highly innovative. They spent 28.724B on R&D, which is about 10.5% of operating expenses.
- Microsoft is a US company that has not been considered particularly innovative. They spent 27.3B on R&D, which amounts to 22.4% of operating expenses.
- Samsung is a South Korean company reputed to have spent a great deal on R&D. They allocated 19.6B USD to R&D, about 11.6% of operating expenses. While Samsung spends more than Apple on R&D as a percentage of operating expenses, they spend far less, in both absolute and relative terms, than Microsoft despite having a higher overall budget.
As for Israel, its GDP (488.53B) is smaller than the combined operating expenses of the above companies (564.4B), and that "gigantic" 5.57% spending on R&D (27.2B) is smaller than the R&D budget of just one of the US companies. Israel defense spending does not help explain its R&D spending because defense spending is tiny in comparison, worth only 21.7M USD in 2021.