Types are controversial because we can't measure engineer productivity. Full stop. I see people on here arguing that they are faster one way or the other, yet we have absolutely no empirical evidence for such a claim. What makes it more complex is that "fighting with types" often takes one out of the flow in a different way than usual progamming challenges. Since it's unmeasurable, we cannot see the effect of product…
I think from an empirical mindset we have to grant that the lack of evidence probably means there is no significant advantage. Because there have been lots of studies, we can't simply say we don't know if there's an effect, or we don't know how to measure it.
We don't know if there's an effect, because we have no way at all to measure it without costs so staggeringly large no one will ever try. We'd need similar engineers, doing all the same practices, with the same stories, and just one difference. But then the engineers would need to have been selected to be similar skill and speed previously, which would require doing other projects with all fixed practices and languages to measure developer skill relative to peers. This also doesn't take into account team cooperation and morale, creative thinking around problem solving, etc. It's a bummer, but without some breakthrough in AI research allowing developers to be measured based on the code they write, it's seeming more and more like an unsolvable problem.