The replication crisis shows that in social science even the subject matter experts are often talking out of their ass, even when they get reviewed by other experts. You can't fix a field full of charlatans if you don't let "laymen" argue with the "experts" of said field.

STEM experts reach the level of proficiency you talk about, but social science experts usually don't, so I don't see anything wrong with laymen arguing with social science experts on equal grounds. Especially if the laymen here knows math and therefore understands the quantitative parts of social science better than the social science experts themselves.