I deal with chronic pain and I’m at the hospital or clinic frequently, often multiple times per week. As someone who is in that environment quite a bit, I can assure you that the dangers of obesity are very clearly and openly discussed; frankly, you can’t walk two steps in a hospital without seeing some sort of PSA about the dangers of obesity.
Your mental model just doesn’t track with what I’ve seen again and again in reality.
The people being told to shut up about it are usually abusing strangers or enemies, and feel very abused and targeted for being criticized for targeting and abusing people. If you were talking about being fat with someone you obviously care about and cares about you, they'd take it in that spirit. If you shamed them for it, they'd hopefully end that fucked up abusive relationship. The only thing I would ever shame a loved one for is their abuse of other people. Otherwise, I want to lift them up, not tear them down.
Then it becomes (well, became) the next taboo that nobody wants to touch with a 10 feet pole since its playing with a PR suicide.
And so we have the world we have, and we reached it step by step by exactly this logic. Simple thing is, fat people need help from society just like drug addicts, yet everybody desperately tries to avoid this framing, and thus help is often not deemed necessary/worth the risk of offending. Thus people die needlessly just that somebody doesn't have hurt feelings.