In economic history, there are few efficient industrializers. Even within Europe, which generally industrialized first compared to the rest of the world, you find mostly ineffective industrializers - the mediterranean region, for example, is populated exclusively with late industrializers. European or not, some latecomers ended up industrializing successfully, Germany and the United States stand out in this regard. Conversely, Latin America, generally speaking, might stand out as a particularly ineffective industrializer, not only industrializing late but also not industrializing particularly successfully.

Industrialization is strange process in that the benchmark is often perceived as the most successful case: Northwestern Europe. It is common, but not always helpful, to expect industrialization to occur in the rest of the world like it did in England or the Low Countries. This is unhelpful because ultimately it means the answer to every economic question can become, “Because we are not talking about England or the Low Counties.”

The Economic conditions which drive entrepreneurs to seek efficient returns on capital investments (at its heart, what industrialization is) do not always exist in the rest of the world as they did in Northwestern Europe. This is particularly true in Latin America, which up to the turn of the 20th century had been able to achieve a fairly strong degree of relative economic prosperity in a mostly agricultural economic landscape, bereft of industrialization. This isn’t exactly a unique case (Italy, by comparison, remained the third-most productive economy in Europe well into the first half of the 19th century also without having industrialized significantly) but it does cut an economy off from the exponential growth which comes in later stages of industrialization (this is where the break-off really occurs: England and the Low Countries experienced a sort of slow-but-steady economic growth taking them to the top spot in Europe before exponentially taking off in the second half of the 19th century and really decoupling from the rest of the continent - they wouldn't be surpassed until the United States did just that in the 1920s). It is difficult but not impossible to jump directly to this second “exponential-growth” stage of industrialization with a very short slow-and-steady phase (the United States and Germany are two countries who did just that) but net of astonishing luck, it takes deliverate planning and forward-thinking policymaking to identify where gaps are and finding ways to mitigate them (Gerschenkron, an American economic historian by way of Russia, called this process “Identifying Substitution Factors”). Latin American policymakers did not take any actions linked to developing "Substitution Factors," probably because they felt they didn’t need to: the capital-owing class was able to develop ever-growing portfolios of agricultural investments which were able to sustain a satisfactory level of economic growth (there is an ambiguous, or possibly even inverse, correlation between agricultural prosperity and industrialization). In Latin America, society’s scales were also never tipped towards laborers the way they were in other economies, further reducing capital owners’ incentives to develop productivity: having technology available is one thing, but feeling the need to to use it is on a widespread scale is quite another.

This is a long-winded way of re-iterating Douglass North’s conclusions that the ensemble of institutions, be they political, social, or economic, which characterize a society are what will determine its success in economic development, which in our era corresponds to industrialization. Your question is interesting in that you correctly hone in on industrialization as the key component to developing a modern economy. Broader (and more common) questions soliciting comparisons between “Anglo” postcolonial states and “Latin” postcolonial states can be reduced to this very difference: However misguided and ineffective Latin American policymakers’ decisions were in the 20th century, they ultimately stem from the single problem of not having achieved truly industrialized economies by the turn of that century. Why didn’t they? Well, in part it’s worth re-iterating the very first point I made; they are not the nations of England or Belgium, and so would always have industrialized differently, but also because their institutional characteristics were such that they did not feel the incentive to industrialize (or at least, they didn’t feel the need until it was too late). And if you look at per capita income, it’s easy to see why: While remaining largely in the slow-but-steady phase of industrialization (or pre-industrialization) many of the larger Latin American economies are nonetheless just a few percentage points short of matching industrialized Europe right up to the 1970s.

There is also a deeper question murmured in some economic history circles which asks, “But how prosperous was Latin America at the turn of the 20th century, really?” However impressive Buenos Aires, Rio de Janeiro, or Mexico City might have been in at the turn of the 20th century, did these cities represent the whole of their respective countries? Are millions of disenfranchised people, many of them indigenous, accounted for in estimates of economic development? Did most citizens even have access to the same economy which built these impressive urban environments? Or, is our estimate of economic development, and thus our perception that these economies may have been on the cusp of industrialization, based on the numbers we have from the europeanized postcolonial core rather than an in-depth estimate of economic conditions across the whole of the various Latin American countries? If so, is it possible that the state of economic development (including industrialization) was deemed satisfactory up until the mid20th century precisely because we are only considering a small component of these economies?

An easy short answer that you might be looking for is ultimately linked to the postcolonial heritage and experience, which is the incipit of the “Institutions” I keep mentioning. This is summarized in Stanley Stein and Barbara Stein’s The Colonial Heritage of Latin America (which explains how, “it is not surprising, then, that Latin America did not begin to modernize its economy through industrialization until a century after independence”). I instead have chosen to spend more time drawing conclusions linked to more general principles of comparative economic history because I think a broader answer is what you’re interested in. And besides, Latin America is enormous, larger than a continent, after all. So I didn’t want to focus too much on, say, Argentina, and talk about specifics which wouldn’t be applicable to, say, Mexico.

Anyway, another interesting examination of North and South American economic history you might be interested in is:

R. J. Gordon, The rise and fall of American growth, Princeton University Press, 2016

And a more general and classic look at industrialization which examines in detail the "late" industrial revolution where the United States really came onto its own (and others didn’t):

A.D. Chandler, Scale and Scope, Harvard University Press, 1990