Technically you could create a static webpage from the WordPress one.

Not only you can, but in many (if not most) cases you should - because of performance and security benefits. The drawback is your site will no longer use the built-in WP search functions, but there are ways around that.

Couldn't you put WP behind a reverse proxy and cache the hell out of it?

We cache the hell out of our WP marketing site. Cloudfront > Varnish > Apache > OPCache > MySQL Query Cache. It feels fast to visitors. People in the admin area still suffer.

WordPress themes are notoriously bloated and 1/4 of the web is powered by WP.

As a developer I'm not too happy about the trend I've seen in the past couple years of 'monolithic' WordPress themes with tons of JS and other code, because making even simple changes to them can get extremely complicated. I think they caught on for two reasons (1) they often have interactive 'builders' that come with widgets you can drag and drop (contact forms, slideshows, etc.) and (2) The whole design trend of things that change as you scroll--'parallax' elements and dynamically-resizing headers, etc.

I've always made my own themes, and even those can be fairly slow without the standard caching plugins. Optimizing Craft CMS sites was a breeze by comparison.