The rendering process for browsers is very well defined, and has a very rigid definite ruleset where (virtually) every accountability is noted and handled. This is not optimal for Machine Learning, which works when we have a large pool of examples, and we don't know the ruleset; it will figure it out. Even if you were to train an Neural Network to process that input, there are several things you must account for:
1. Variance in data.
Not all webpages are equal in length or complexity, and making a neural network to generate output from HTML would produce garbage most of the time.
2. Training time.
The time it would take for a neural network to understand HTML tags, attributes, the DOM Tree, and each and every element, including new ones being added every few years, and how each one renders and behaves, would take an extremely long time, most likely several years on a fast computer, if it even were possible
4. New Standards
Not all HTML is equal, because of different standards. WHATWG began working on HTML5 in 2004, and browsers started to implement not long after. In 2004, there were very few examples of HTML5 sites to train your network to begin with. Sure, now it's standardized and every website uses it, but what about HTML6? When the first specification is released (probably 2017-2025), virtually no websites will use it, because no one will support it. Only when it finally becomes standard, probably in the late 2020s or early 2030s, will you have enough data to train your monstrous system of neural networks
Trying to solve HTML rendering with Neural Networks is akin to trying to nail a nail with a screwdriver. It's just not going to work
Hope this was helpful!