1. Someone _has_ come up with the One True Layout System. It's just that most people like to pretend TeX doesn't exist or, when they grok the box-and-glue layout model, try to reinvent it from scratch.
Someone yell at me if I'm wrong, but isn't TeX designed for paged content?
That means while TeX might work amazingly for paginated content, single page apps, or really any non-paginated content, is very much a screwdriver where a hammer should be used scenario.
Overall it is, but when the above commenter mentions box-and-glue, they're talking about the building blocks of the line breaking algorithm TeX uses (you can read about it in this paper: http://onlinelibrary.wiley.com/doi/10.1002/spe.4380111102/ab... ). The box-and-glue system is a way of expressing a layout as an optimization problem (in the paper, they talk mostly about determining line breaks within a paragraph, but the idea of minimizing badness can be extended to determining page breaks as well). A bigger concern for me is the performance of laying out any reasonably complex page — the performance we get from rendering a reasonably complex webpage today is generally much better than rendering a reasonably complex LaTeX document.
I've come across a feature request for Firefox where someone proposed to use the Knuth Plass line breaking algorithm just for text layout, but they didn't get very much traction: https://bugzilla.mozilla.org/show_bug.cgi?id=630181
Are there any CSS replacement proposals that are based on linear programming [1]? There are a lot of things you cannot solve with just LP (e.g. rearranging floats on a page) but it's a pretty good -- and simple -- abstraction for laying out boxes relative to each other.
Solving LP is fast, especially when many of your constraints are equality constraints (as would be when specifying tables).
I think Cassowary [1] is what you're talking about (particularly section 1.2 where they talk about some modifications to make their system very fast for incremental updates). Apple has based their constraint-based layout system, Autolayout [2], on Cassowary. There's also a project that incorporates Cassowary constraints into a CSS-like declarative syntax called GSS [3].
does TeX have responsive layout with a variable document width? For the past year my ability to use CSS alone to convert an existing HTML Website and make it work on mobile has been putting food on my table. Could I be using TeX for the same thing?
In theory, yes. TeX basically outputs DVI. DVI is meant to be a 'DeVice-Independent' format, so someone could come up with a browser layout engine that implements it, thus giving Web pages TeX-like typography and layout quality.