There is tension between two fundamental ideas: is the server offering content and allowing the client to interpret it as they see fit; or is the server offering an experience that is out of the hands of the user?
Out of these two conflicting ideas come all sorts of issues. Accessibility is one, but so are things like scraping, copy/paste, DRM, confidentiality, artistic integrity, cross-platform compatibility, new devices, peformance & resource consumption, etc.