tl;dr: SE pages break almost all browser "reader modes." Reader mode is designed to allow users to customize the appearance and formatting of a web page to meet their reading needs. Since it is impossible for a fixed design to equally accommodate all users, I propose investigating whether the HTML structure of SE pages could be modified to play nicely with browser reader views.
Edit: I opened a question on StackOverflow exploring the technical reasons/solutions for this incompatibility.
Relation to recent change in post formatting (line-spacing, background-color): This is neither for nor against the New post formatting, but it is related in that when you tap the native "reader view" in a browser,* often all that's readable is the question or the first answer; the other content simply isn't there. This means users cannot rely on reader view for SE sites. The developer effort spent making SE's design accessible could be partially directed toward making SE compatible with standard tools.
Discussion: Every browser implements "reader view" differently, but most reader views nail the majority of "article" style sites, while nearly all fail on SO/SE posts. I'm not sure what the underlying mechanics are, but from (informally) comparing sites that work/don't with reader view, it seems that they have a heuristic like "look for the element with the most text," and display that to the exclusion of all others. The SE/SO separate-questions-and-answers format seems to break these readers.
Next Steps/Toward a solution:
It might be possible to reverse engineer the success conditions well enough to all most or all of the readers to parse these posts. Some iterative poking around in browser devtools (change to page structure, view in reader, repeat) could reveal a solution.
Also, I believe that Chromium is open source, so perhaps digging into the code base could reveal the rules for reader mode.
Also related: Re: line-spacing: Please revert the line-height change!, Request for a possibility to adjust the spacing between lines for those with poor eyesight, Re: block-quotes/background-color: Please revert the quote background from white to yellow
*Appears to apply to both mobile and desktop reader view in Firefox or Safari, and "simplified view" in mobile Chrome and Edge, which don't have a native desktop reader view. I haven't tested this comprehensively, but I use all of the above browsers daily in app development and have some familiarity with all of their "reader view" modes. Edit: according to a comment, Firefox handles this better than other browsers.