I guess there are two bits here — one, does shame work on an individual already emotionally invested in a culture, and two, does shame work on a more holistic level for those people who might be attracted to a culture? You may very well be correct that you can’t shame individuals particularly effectively — SJWs screaming “racist” at straight white males haven’t created a wave of SJW converts from NRA members, for sure.
But that being said, SJWs have driven a lot of the culture in academia over the years, dramatically changing the political makeup of university professors, so to a certain degree, shame does seem to work on a larger level. This isn’t to say that SJW college students never grow up to regret their youthful bigotry, or that university professors will always be overwhelmingly liberal, but shame certainly seems to have some demonstrable effect on the larger level.
I would argue that you’ve got a few good places to start listed, but I’d disagree on some details — healthy food means low-carbohydrate high-fat, and we could do a lot about the root cause of kids without fathers if we supported marriage as an institution, and made it much more clear the severe disability we put on children when we have them out of wedlock. We might not be able to shame the single mother into not having another child out of wedlock, but maybe we can teach the children of those single mothers that they don’t want to make the same mistake their parents did, and change the culture moving forward.
I expect the government’s role in this holistic approach would be more about rescinding existing legislation and programs that are faulty, rather than creating new institutions, but I’m sure people who believe in big government would have a different opinion :)