Part of the problem with discussions in many societies now is this false equivalency. Yes, some people might be driven to suicide due to shaming, but this is not the vast majority of people. However, NOT shaming people about their weight leads to a much larger portion of the population being fat and unhealthy, which has incredible downstream health and societal impacts.
So I disagree with your equivalency here - shame is a good social tool for the majority, and while we should certainly be on the lookout for the extreme minority who have mental health issues, we should not be throwing out good general social tools just because of a few edge cases.