1. Concerning economic studies, there are many and from diverse perspectives. One group concerns the so-called “Motivation-Hygiene Theory”, some notable sample studies include:
Lundberg, C., Gudmundson, A., & Andersson, T.D. (2009). "Herzberg’s Two-Factor Theory of work motivation tested empirically on seasonal workers in hospitality and tourism." Tourism Management, 30(6), 890-899.
Bassett-Jones, N., & Lloyd, G.C. (2005). "Does Herzberg's motivation theory have staying power?" Journal of Management Development, 24(10), 929-943.
In the education field, there’s a mountain of studies but I’ll leave it to you as a classroom googling exercise.
As for “The context is important” … I see you want to spin it. Think before you spin. Consider that maybe all your core capitalist beliefs may be wrong.
2. I used the USSR and China as examples of superior economic systems to show that one can do better and not for inequality purposes. The USSR was completely government controlled while the Chinese is now about 50-50. The 50% government part is just as productive and, critically, it stabilizes the system so that the recurring recessions, collapse or near collapse every few years are avoided. China has had about 40 years with not a single recession unlike ‘capitalist’ economies.
And your understanding of capitalism is wrong. The difference between various forms of socialism and capitalism is NOT markets. They all have markets in pretty much the same way. Indeed, even feudalism and kingdoms have markets. The difference is the ‘command’ or ‘decision-making’ structure of the workplace. Capitalism has the employer being individuals called capitalists while socialism has government or cooperatives as the employer.
3. Concerning inequality, China has severe inequality problems but this is mitigated by extensive social programs and support at levels much higher than the leading economy, the US, where the per capita income is more than 3 times higher. In the US, they don’t even have universal health care!
As for the Gini index in China, the problem is that China started at a very low economic level and the cities subsequently exploded in prosperity relative to rural areas. However, the government of China eradicated deep poverty by uplifting more than 800 million people economically in a feat fit for the sagas. No other country managed to do that. The high Gini index is due to this ‘division by zero’ between urban and rural rather than stratification within primarily urban centers. For citation, see:
Chen, J., Pu, M., & Hou, W. (2019). The trend of the Gini coefficient of China (1978–2010). Journal of Chinese Economic and Business Studies, pages 261-285.