I’m not sure this is only about regional variations (I wrote about before) where in North America liberal refers to modern liberalism whereas for the rest of the world it typically refers to classical liberalism. Regardless of their thoughts on classical liberalism, there’s still the concept that “protecting and enhancing the freedom of the individual” ought “to be the central problem of politics” or rank high up there, and that concept has a name: liberalism. Acting like there’s some fault in insisting freedom of the individual matters or that it has do with anything else is a shitty take on their part.

To address your other points, neither capitalism nor liberalism is essential to each other, and capitalism is older than liberal democracy.

Capitalism emerged in Britain, the Netherlands, and most of today’s high-income countries long before democracy.

Even in the recent past, capitalism has coexisted with undemocratic rule, as in Chile from 1973 to 1990, Brazil from 1964 to 1985, and Japan until 1945. Contemporary China has a variant of capitalism with a high level of state intervention, but its system of government is not a democracy by our definition. In many countries today, however, capitalism and democracy coexist, each system influencing how the other works.

Moreover, modern liberalism advocates market regulation.

Liberal democratic governments may play a major role directing economic development even with less left-leaning liberals.

These differences even among democracies are part of the explanation for governments’ differing roles in the capitalist economy. The Japanese and South Korean governments play a central role in setting the direction of the economy. But the amount of tax collected (both locally and nationally) is low compared with some rich countries in northern Europe, where it is almost half of GDP. In Sweden and Denmark, the tax system is used to reduce income inequality to a far greater extent than in Japan and South Korea.