There is a difference between what institutions allow and what they require. If in a capitalist society everyone is convinced of the desirability of one common goal, there is nothing in the structure of capitalist institutions to prevent them from cooperating to attain it. Capitalism allows for a conflict of ends; it does not require it.
Socialism does not allow for it.
That’s the nature of collective decision-making, whether on a national scale (such as classic socialism) or on a smaller scale (such as government intervention into this or that industry or type of consumer choice): every individual must abide by the rule dictated to, or decided for, everyone in the group.