> It would be better if the web browser world had pixel level render targets
We also have escape hatches when you need pixel controls: Canvas, and webGL which can be rendered to a Canvas. The only difference is that they're not the core that HTML is based on. This is on purpose, because using Canvas should be very rare. You should embed your (rare) pixel-based rendered component into an HTML tree with appropriate non-visual markup around it to describe what it is and what it does.
Pixel-level render targets are a design antipattern for most apps. Not all apps (games for example), but the vast majority of them.
To me this isn't a design thing -- it's a purely practical decision. Your app state needs to be accessible to people, people need to be able to build on it, programs need to be able to parse it and manipulate it, it needs to be responsive when high-definition displays or Apple Watches come out in the future, and it needs to degrade gracefully when parts of the browser stop working. We've been able to observe for a long time that apps that are built this way are better for end-users.
In the browser, text is your pixel. Of course you are welcome to build things on top of that with CSS, images, and Canvas. More to the point, I'm not saying that 95% of the time you should abandon your design and make a minimalist terminal interface -- I'm saying that for 95% of the phone apps and native apps I see, HTML would be fine. There is a pretty good chance the design someone has come up with is already representable in pure text, and they just haven't thought hard enough about how to do it. I'm not saying design everything minimalist, I'm saying your design is probably already a lot more minimalist than you think, and it probably wouldn't be that hard to separate content from pixel-positioning and style for most apps.