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"social cost" is correct and can be used in written English.
It is a term used to refer to the negative effects of a policy or action on people or society, such as financial costs, environmental degradation, or health impacts. For example, "The social cost of burning fossil fuels is leading to climate change."
Exact(58)
There is, therefore, a great social cost.
"The social cost is immeasurable.
The traffic also brings a social cost.
Then there is the social cost.
It can be the social cost.
But that progress will come at some social cost.
They accrete to a fairly sobering social cost.
The result was "The Problem of Social Cost".
"Calculating the social cost of carbon requires many, many assumptions".
Although it proved a success, the social cost was high.
Conservatives are asking him to rein in spending, no matter what the social cost.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com