The question of why Song China didn't cross the line, so to speak, into genuine industrialization gets asked every now and then; here is a good answer. With regard to the economic aspects of this question - that is, inasmuch as you're asking about capitalism rather than industrialization - I'm less sure that it's been addressed before, but a lot of the factors explaining the lack of industrialization may apply to that too.

As explained below, counterfactuals can be tricky to answer definitively, but a key reason why industrial capitalism never took hold in Song China might be explained by just why it did take hold in post-renaissance England and France. In a way, it's better to think of capitalism in this time period not as the ability to run a state apparatus better than Imperial China, but the inability to do so, and the struggle to try and match that imperial level of wealth and control in government.

Industrial capitalism starts in the era of mercantilism, which was more or less defined by the crowns of various large, consolidated countries selling monopoly rights to private producers in exchange for the exclusive ability to offer a product or service across the realm. This was made possible by the central state being just sophisticated and powerful enough over all of its territory to be able to enforce a monopoly uniformly. France was the gold standard when it came to this sort of thing. Monopolists would bid up the price of the monopoly for their good, the King would grant it, and use some of the money to pay state agents in all of the major cities to ensure that only this monopoly producer's goods were being sold and used. The state wasn't sophisticated enough to audit individual or business incomes to levy income taxes like we take for granted today, or at least not in any reliable fashion, and the French state realized that checking rural areas for contraband goods would be even too much effort for the returns they could expect from doing so. Having tons of towns and cities as commercial bottlenecks allowed the Kings Louis of France at the time to extract maximum revenues using this new, blunt, and effective tactic of monopoly selling.

England tried this, but... England sort of sucked at it. One reason for this was the ineffective nature of England's enforcement mechanism. English dispute arbitration was done by unpaid locals, instead of centrally chosen, highly paid enforcers, making monopoly restrictions easy to flout entirely via bribes or local influence. But more importantly, by this time, England had already gone through hundreds of years of having a competing monarch and parliament, struggling over who should have the power of government in the state. To raise funds for the crown, the king or queen would try to grant the same monopolies that the French kings were granting to private producers, but Parliament, with its own courts and enforcers across the country, would often void the crown's monopolies, and try to sell their own! In the midst of this confusion, unsanctioned producers of monopoly and guild-protected goods would often set up shop just outside the jurisdictions of major cities, forming "suburbs" of sorts where city dwellers could get what soon became lower priced and higher quality goods than the monopolies could provide. It was really only once English domestic mercantilism proved to be a massive failure, from both an output and a revenue perspective, that writers like Adam Smith began theorizing on different methods of fueling the country's economic growth. Simply as a means of raising tax revenue for the people in charge of the government, Parliament and the crown pivoted to the domestic free market and export-oriented foreign policy that built the capitalism we know today.

France, while being able to develop industry quite successfully at the same time, soon fell behind English growth rates, largely because it was too successful raising revenues through its monopoly sales. And while France wasn't absent in the Age of Exploration, it was less reliant on export revenues and colonial profits than Britain, making innovation and technological improvement less imperative for French industry early on. For a Song Dynasty with a fairly sophisticated government, long-established trading partners, and very few nearby places they could conquer and force manufactured goods upon that would size up anywhere close to their own domestic economy, it's unlikely that they would find the need to have firms consolidate and compete with eachother for surplus production.

Source: Ekelund, R. B., Jr., & Tollison, R. D. (1981). Mercantilism as a rent-seeking society: Economic regulation in historical perspective. Texas A & M University Press.

This is a difficult question to answer straightforwardly because it is really asking about several things on which is there no historical consensus: the origins of the Industrial Revolution, the origins of the "Great Divergence," and the origins of "capitalism."

On the first point: /u/TheRealRockNRolla has already linked /u/cthulhushrugged's excellent write-up on "industrialization" under the Song. While the Song made use of some labor-saving technology (water mills, etc.), they were ultimately reliant on manpower. But the key hallmark of the modern Industrial Revolution was the systematic and continuous development of labor-saving technology through the exploitation of alternative energy sources (chiefly the fossil fuels: coal, oil, gas).

So the Song didn't really industrialize. But then, why not? This is inherently a comparative history question. In order to ask this, we must ask why Britain did industrialize in the 18th century. While there are a number of competing theories about this, there is ultimately no real academic consensus on this in the field of economic history.

Perhaps the explanation with the widest reach is that of Robert C. Allen. Allen starts with a very ordinary economic proposition: labor-saving technology reduces labor costs, but also increases capital costs. This kind of technology is most profitable in scenarios where things like energy costs are low and labor costs are very high.

Britain had very high labor costs in the 18th century. This is due to a number of factors, but Allen places stress on the expansion of export-oriented colonial trade. This trade increased demand for manufactured goods and shifted the British economy towards manufactured goods, increasing both urbanization and causing a tight labor market that led to higher wages. Growing urban demand also led to an "energy revolution" that precipitated the development of a significant coal industry.

So Britain had both a high-wage economy and very low energy costs owing to large coal deposits and a significant and active coal mining industry. This, according to Allen, is the primary explanation for why British industrialists began to introduce labor-saving technology into their manufacturing processes.

China, by contrast, has historically been a low-wage economy. This has traditionally been attributed to a low land-labor ratio, but the exact causes are not necessarily important here. Per Allen's reckoning, China also had very high energy costs; see his figure here (from Global Economic History). Even at the height of the Song, it was cheaper to employ more manpower than it was generally cheaper to just hire more manpower than it was to develop and then deploy labor-saving mechanization.

Of course, this explanation for (non-)industrialization and the Great Divergence can be reasonably disputed. In the early 2000s, the California School (typified by Kenneth Pomeranz) pushed back against this interpretation of the Chinese economy, arguing that certain areas — namely, the Yangtze Delta area — had similar wage levels to Britain, but there is also now a fairly large literature reinforcing the view that China had a low-wage economy compared to Britain (see: see Allen, Bassino, & Ma, et al, "Wages, Prices, and Living Standards in China 1738-1925")

So that covers the industrial side. But what about the "capitalist" side? This is even more difficult to answer because capitalism is a nebulous term that has a variety of meanings depending on what theoretical orientation you come from. Even from a Marxist standpoint, where the term is perhaps the most coherent, there is absolutely no consensus on how or even where capitalism first developed.

Perhaps most relevant to your question is the "sprouts of capitalism" thesis. This line of argument, developed by Chinese historians, holds that at various points in Chinese history there were points where one could see the beginnings of capitalist development, which were nevertheless held back or reversed for various reasons. The Song efflorescence would be, in this view, one of these "false beginnings."

I think this is basically a fair characterization, despite the pushback it's gotten from some western Marxist historians. To be sure, the Song Dynasty was not a society "in which the capitalist mode of production prevails," but it seems indisputable to me that certain industries in certain regions were basically organized along capitalist lines. For example, from von Glahn:

Coking and steel-making operations required substantial capital resources but also yielded significant economies of scale. The thirty-six private foundries at Liguo in northern Jiangsu employed an average of 100 wage laborers engaged in mining, coking, smelting, and refining tasks, and together produced nearly 7,000 tons of iron and steel per year. Total annual output of iron and steel in the late eleventh century has been estimated at roughly 125,000 tons.

So why didn't Song develop into a (pre-industrial) capitalist economy tout court? Again, this is difficult to answer straightforwardly because there is no consensus. The unsatisfactory answer to this part of your question is that there was no transformation of the countryside in the Song Dynasty. Pretty much everyone agrees that for capitalism to predominate, the peasant economy must be dissolved: you need to "free" people from the land to get them working as wage-laborers. Whether this dissolution comes, à la Robert Brenner, from class struggles in the countryside leading to insecure land tenure, or through commercial incentives coming from the cities and global trade, is more difficult to answer.

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Allen, Robert. The British Industrial Revolution in Global Perspective.

Allen, Robert. Global Economic History: A Very Short Introduction.

von Glahn, Richard. The Economic History of China: From Antiquity to the Nineteenth Century.

Hey there,

Just to let you know, your question is fine, and we're letting it stand. However, you should be aware that questions framed as 'Why didn't X do Y' relatively often don't get an answer that meets our standards (in our experience as moderators). There are a few reasons for this. Firstly, it often can be difficult to prove the counterfactual: historians know much more about what happened than what might have happened. Secondly, 'why didn't X do Y' questions are sometimes phrased in an ahistorical way. It's worth remembering that people in the past couldn't see into the future, and they generally didn't have all the information we now have about their situations; things that look obvious now didn't necessarily look that way at the time.

If you end up not getting a response after a day or two, consider asking a new question focusing instead on why what happened did happen (rather than why what didn't happen didn't happen) - this kind of question is more likely to get a response in our experience. Hope this helps!