Plain HTML documents are SEO friendly, are a11y friendly almost by default, back/forward navigation works, and HTML doesn't chew battery and bandwidth on JavaScript.
For our web app the biggest pain points are: security (hard to integrate third party libraries), control over the viewport (an app header and footer that don't get lost when zoomed - like an App), control over data entry (the hacks we have to do for fast reliable time and date entry are rediculous, and other stuff is just too hard), and control over navigation (browser back/forward is broken for applications that POST data).
Unfortunately Google don't seem to want to encourage plain HTML documents (instead the insane AMP shit).