Since there isn't a solution to the minimum wage dilemma within the framework of a capitalist society (too low and workers suffer, too high and capitalist enterprises can't function), why don't we just let the workers manage the means of production?

If workers manage the means of production, all decisions are made in favor of the workers. Workers only see their self-interest, rather than the goals of the organization. They are likely to increase their wages, which would increase overall costs for the organization. This would lead to a decline in profits. With the decrease in profits, the organization would have trouble staying on the market. The increase in the workers' purchasing power would also discourage them from working efficiently, which can further decreases the organization's productivity. These are reasons for which workers should not manage the means of production.