The argument that advocates of 'capitalism' are making: that "free markets support the social good", is in a qualified sense the same argument you're making.

To explain why let me first challenge how you're defining the capitalism:

People often conceptualise "capitalism" as the existence of something. They latch on various business-related qualities to its definition, like: the pursuit of profit, large corporations and monetary transactions. But that is not what capitalism is. In reality, capitalism is the free market. It is the absence of authoritarianism.

A free market is a society that enforces the precept that we have an inherent right to engage in consensual activity, and to make exclusive use of natural resources that we legitimately acquire (with what confers legitimacy to natural resource acquisition varying greatly amongst free market advocates). It is the only ideology that I have found that is both humanistic and consistent.

An anarcho-leftist will argue against the right to appropriate natural resources. But when challenged, will admit that a person has an inherent right to make exclusive use of natural resources if it is utilized in the form of "personal property", or a human body.

A utilitarian will argue that the only thing that matters is maximizing benefit to the majority. But consistent application of this ideology is necessarily unjust, as there will be cases where injustice to a few benefits the majority.

Anyway, in the absence of authoritarianism, economic activity anywhere on the left-right spectrum can be pursued, including voluntary forms of all of the economic structures leftists advocate for (e.g. a voluntarily formed welfare program is possible, but one that taxes those that did not opt-in is not). So insofar as you think that an economic system that enables any form of consensual economic relationship provides the best environment for creating the solutions that support the social good, you are fully in agreement with "capitalism".