People all review differently. Some reviewers are only active if they have something good to say, and then some people only review if they had a lousy experience. Some are way into the social aspect of yelp. Yes, there is a social scene of reviewers in the yelp community.
You can't really do much about how people come to their conclusion about your business. I've seen reviews of other places where the people are reviewing a place they have never been to. How does that work!? Its like they are commenting on the idea of the place, and not their experience.
I imagine many reviewers are influenced by what other people, either in their own dining party or out, think about a place they are about to review. Should that be relevant? "I had a friend who ate here and had the same experience..." Maybe, maybe not. I mean, its a review based on "your" experience, right? I think the same goes for public info like HD scores. I could see them being useful as a reference to a feeling you had while in a restaurant. Like "wow, despite its reputation, I found this place to be immaculate and professional. They must take criticisms to heart and improve where needed."
But as a way to kind of pull away the curtain on a system like HD inspections as a way to draw more negative criticism to a business because you may have a chip on your shoulder is kind of harsh.
In my experiences as a cart owner, my super positive, 100% passing (or nearly) inspections would not really tell a consumer much about what to expect when eating at my establishment, in my opinion. Only that I follow the rules. On the flip side, I could see how a barely passing inspection would have all kinds of interesting juicy comments for people to judge.
So, I don't think this info would give people a very balanced approach to helping them figure out if they should eat somewhere. But it might tell them where they might want to steer clear of if there are egregious repeat offenders of the HD rules.