Who sneered at attempts to make things accessible?
So I'm genuinely curious: when is it better to not use semantic markup?
It never is - but nevertheless it happens all the time. Perhaps you hadn't noticed it was exactly what this article was about?
When the tech is both widespread and affordable, you can start designing for the tech.
Don't even understand what bothers you so much about making pages more screen-reader-accessible in the first place. Great, I'm glad that you have experience in this area and can attest to the fact that screen readers don't always work even when HTML is semantic. But why are you actively resisting semantic HTML?
It sounds to me like you're saying, "It doesn't work well, so we shouldn't usw it at all." What would you prefer, div soup?
It doesn't even need to be the case that semantic HTML is a killer solution for screen reader users. Just needs to be better than nothing once you net costs and benefits.
So I'm genuinely curious: when is it better to not use semantic markup? Or when does the cost of using it become prohibitive?