Well, it's certainly not limited to killing off characters, but people have been writing about emotional release as a response to tragedy in drama for quite a long time. Generally it's thought of as a good thing, if not necessarily a pleasant one, and I'm inclined to agree with this analysis; people go into fiction looking for an emotional response, and the enduring popularity of tragic storytelling suggests that they aren't exclusively looking for emotions generally regarded as positive.

Content warnings pointing to what a work's going for might not be a bad idea from a utilitarian standpoint, though. I personally handle tragedy well, for example, but I have a lot of trouble with cringe comedy.

Well, one of my favorite authors is infamous for doing this, and I for one think his works are the better for it. It certainly hasn't prevented them from becoming very popular.