it's not like it's a free speech issueWhy is it unrelated to free speech? It seems like it would be a free speech issue if pre-accident images weren't allowed to be published, e.g., in a news article about the accident. I don't see a material difference that would take accident photos out of the domain of free speech.
For my part, as a parent, I would never want to look at such photos. I would however be alright with their use, for example in safe driving campaigns in drivers ed courses. I believe some driving courses (specifically against drunk driving) have done exactly that. I'm sure other families would feel differently, but I don't think there's a prima facie case to be made that no family ever would be okay with this and that it would always increase the emotional toll, or never have any benefit.
I certainly don't like them being published merely to satisfy the morbid curiosity of random internet folks, but I also don't see how you ban that without potentially running afoul of (US) free speech rights that have strict limits on speech restraints. Obscenity is one of those limits, but the law has continually struggle to find a bright line rule by which to measure such things. At a minimum, that lack of clarity still places this sort of image within the domain of free speech issues.