> It would be nice if there were some smaller browsers that didn't focus so much on backwards compatibility

There are lots of those.

> but on leveraging the most important features so that most of the web could be browsed, still without sacrificing end-user security by implementing each and every feature and performance tweak.

That's simply not possible. Even if you restrict yourself to the Alexa Top 100, browsing is impossible without implementing most of HTML5, JS, CSS3 (media queries + gradients + borders + flexbox + ...), SVG, etc. Even if you restrict yourself to just Wikipedia, most of the Web platform gets used (including some uncommon stuff like multicol).

If you want this to be viable, you need to convince Web authors to stop using the features you don't like.