1) A site that isn't ready for a screen reader probably isn't ready for a voice browser or other non-visual user agent. Say, an AI/digital assistant. Or perhaps even a search engine indexing bot (though for the last 10-15 years the incentives behind this often mean people will invest heavily, even non-cooperatively, in this specifically).
2) Projects for which the engineering takes into account the possibility of serving content to non-JS or weird screens UAs from the get-go are often better technically. Not a statistically investigated theory, but my theory is that it's because if you're really doing the REST/resource-oriented thinking necessary to make a non-trivial app display responses as minimal markup, you're also doing the thinking necessary to make a good API to be consumed by a dynamic or even SPA front-end. And vice versa: if you've got a good API for a dynamic-heavy or SPA front-end, it's not difficult to represent the given resource with the media type HTML instead of JSON. Which means if it is difficult to represent a resource as HTML instead of JSON, something's probably not right with how your app is put together.
I wouldn't go so far as to say every app needs to be plain-HTML + accessibility focused, but I think there's benefits that go beyond the margins of users with direct accessibility issues.