I think you're underestimating the effects of content warnings. As an example, studios routinely alter films so as to achieve more favorable ratings from the MPAA.
Rating systems have teeth, yes. But the "some viewers may find the following images disturbing"-type warnings, to which trigger warnings are equivalent, don't have teeth. They're voluntary guidance. Think also of epilepsy warnings.
I think plenty of people would alter their content to avoid warnings, regardless of context. But, I only have data for the MPAA and also maybe recordings with explicit lyrics. I don't necessarily think warnings are bad, I just think that in general, if you're going to label people's work in a negative way, some people would rather change their work so that it doesn't get labelled like that. I mean, I try to be polite on HN so that it doesn't get downvoted and greyed out, but this isn't really that bad of a thing.