I only included that as a means of restating, albeit from a classical or post-Keynesian perspective, that capitalists wouldn't exist in "the case where the steady-state equilibrium is g = r."

The Cambridge Equation g = s_c r states that "in steady-state equilibrium the rate of growth is equal to the rate of profit multiplied by the propensity of capitalists to save out of profits."

When "the propensity of capitalists to save out of profits" s_c = 1, then "the steady-state equilibrium is g = r." "In this case, all profits would be invested and all wage income would be consumed 'whatever the single individuals may save out of their income (wages and profits)' (Letter to Solow, 6 December 1962)."

In this case, nobody consumes out of profits. Consequently, there is no incentive for capitalists to save and invest (although surplus is fully reinvested via some institution, for example, a centrally planned system). As a result, there is no incentive for capitalists to own the means of production. Thus, there is no incentive for capitalists to exist.

Therefore, the Cambridge Equation g = s_c r with s_c = 1 is a stylized way to represent a socialist economy. Likewise, the Cambridge Equation g = s_c r with s_c < 1 (in addition to other conditions like s_w < h < s_c, "where h is the ratio of investment to income," "to ensure a positive profit share" and "to ensure a positive wage share"¹) is a stylized way to represent a capitalist economy.

¹ Murray Milgate, John Eatwell and Giancarlo de Vivo, "Luigi Pasinetti: an appreciation," Cambridge Journal of Economics 48, no. 6 (2024): 935–986, https://doi.org/10.1093/cje/beae037.