It's true that functionists might use the particular functional explantion I used as an example, but so do Marxists like Milton Fisk and radical social democrats like Cloward and Piven. To subscribe to taht theory of welfare, at least as part of the story, does not mean you think society is a harmonious whole where everything is happily maximally functiobal. Besides, the theory is true in part.
Welfare does dampen social unrest.