Overall, my source for this answer is general reading of works by Ha-Joon Chang, especially Bad Samaritans, and being educated in a South American country, so there may be bias.

Giving a definite answer on why certain countries end up being wealthy while others don't is extremely difficult. As far as I understand, there is a whole area of economics called development economics that attempts to answer this question, but until now it's hard to say whether there is a definite series of steps that can be taken by a country to become wealthy. Things that have worked in the past may not work today, things that currently work for a particular country may not work for its neighbours.

I would argue, first of all, that it is misguided to think that the US' involvement in South Korea and Japan after WW2 is the, or at least one of the, main reason(s) why these countries currently enjoy high GDPs per capita. The issue is that for any development hypothesis, you can pick countries that fit, but you can also find countries that don't. E.g. the Philippines were literally owned by the US for a considerable time in the first half of the 20th century, but they are solidly in the group of middle-income countries at present. On the other hand, the ROC (Taiwan) prospered as one of the Asian Tigers without much evidence of US involvement. How can these countries be reconciled with a "direct US involvement => economic growth" hypothesis?

Chang's thesis is that it's quite likely that SK's and Japan's high growth in the second half of the 20th century was mainly due to their adoption of Export-Focused industrialization, meaning that industrial production was intended to be consumed not only domestically but also abroad. E.g. in the case of SK, according to Chang, the government took initiative in setting up companies itself with this goal in mind, like POSCO, the steel mill; or supporting existing companies, like Daewoo.

By contrast, some South American economic efforts can be categorized as Import-Substitution industrialization. The example that I know of regarding this is Argentina under Perón's first regime, where industries were set up to produce goods domestically, to be consumed domestically[1]. Also historically, South American economic activity has centered around agricultural or natural resource exports. Could it be that there's some kind of historical inertia, or lack of know-how on to set up capital-intensive industries as opposed to good ol' banana, coffee, and tobacco? I don't know, this is also a hard question.

The reasons why South Korea chose to appoint "technocrats" to its government positions and decide to compete industrially on a global theatre, while Argentina kinda closed itself off to the world are out of my pay grade, and I would say are also questions that may not have a definite answer. I have read explanations ranging from geographical determinism all the way to simply "inherent culture", which is my pet peeve. Chang mentions quips about "inherent culture" by British industrialists in the early-to-mid-19th century when referring to the "romantic" character of the Germans, a "romantic" character that would make hard work and industry impossible in the German territories. Similar quips were made about "lazy" Japanese before the Meiji restoration. Look how those characters turned out.

It's worth mentioning that US-South American relations have quite a lot of history of being exploitative in nature, starting in the late 19th century, through e.g. the Chiquita/United Fruit's shenanigans in Colombia and countries in Central America (like direct involvement of local military forces in suppression of labour demonstrations[2]). Models of US involvement have also been different; while the Philippines was an outright colony, the US' preferred method of involvement over South American nations has been to back coups, or in particularly dire circumstances, invade, and set up a puppet dictator that they let more or less "run free" without absolute supervision as long as the threat of communism is kept under check (think Pinochet). However, I'm not able to speak much on US exploitation/involvement in other parts of the world around the same time period.

Just my 2c, hope this answer is acceptable.

[1] Sorry about the wikipedia link! https://es.wikipedia.org/wiki/Industrias_Aeron%C3%A1uticas_y_Mec%C3%A1nicas_del_Estado

[2] Check out the Colombian Banana Massacre

I tried to answer some of this here, though it is an enormous question: https://www.reddit.com/r/AskHistorians/comments/ewgr0q/in_the_early_80s_south_korea_and_mexico_were/fg3rvfi?utm_source=share&utm_medium=web2x

One thing to keep in mind: Latin American countries aren't really among the poorest in the world. Places like Nicaragua and Honduras are quite poor, but not compared with sub-Saharan Africa or Central Asia, which are by far the poorest in the world. Brazil, Colombia and Peru are only slightly poorer than the world average, and Argentina and Mexico slightly richer. Uruguay and Chile are well above average. This is a pretty weak performance for a region that had higher incomes than all of East Asia in the first half of the 20th century, but that's a metric about growth performance, not poverty per se.

But then, Japan and South Korea are now both fully developed countries with Western European levels of income, so the question is still a pertinent one.