Knuth wrote TeX in the late 1970s because he wanted to typeset material as well as he could, given the limitations of his own knowledge and of the technology available at the time. It's generally agreed he did a pretty good job, but what he certainly was not trying to do is separate structure and style.
Lamport wrote LaTeX in the mid 1980s as he did see the need for a clearer separation of the two areas. LaTeX was revised in the early 1990s, and the current kernel dates from 1994 (with bug fixes, of course). This predates he HTML + CSS model by some time, and again technological limitations meant that to further complicate LaTeX then would have been impossible. (In 1994, LaTeX was almost too large for many PCs, and the team worked very hard to squeeze it down.)
In the HTML world, new tags can be added and will be ignored by renderers which do not know them. That's not the case for TeX: unknown control sequences are errors. So we can't just add new concepts and expect existing documents to work: this is really important. So the decisions made in 1994 still have importance for LaTeX today.
ConTeXt is newer, and does separate out a lot more design than LaTeX 'out of the box'. ConTeXt also takes a different approach to stability to LaTeX, with a more active development outlook for the kernel. However, the ConTeXt approach is in some ways more like plain TeX than LaTeX, in the sense that ConTeXt keeps the design 'closer to the user' than LaTeX does.
Input and output
In the HML world, a document is read entirely into memory to build the DOM for rendering. TeX does not work like that, at least unless we program it all ourselves. Instead, TeX reads a line and processes it before moving on to the next line. (LuaTeX can alter this, but I think even in ConTeXt it's still true that the TeX model is the main one.) As such, the approaches needed to alter appearance are very different.
A key thing to bear in mind when thinking about this area is what people want as output. In the TeX world, we are focussed on high quality typesetting. As such, there will almost always be some manual adjustment of the design to reflect the realities of the content. That's not what happens in 'well written' HTML, and although it can be expressed in XML certainly breaks the strict separation. I and others would argue that this is no bad thing: you do need manual intervention to get the best results.
Tables are specifically mentioned in the question, and I think deserve consideration on their own. In HTML, tables have been used for a variety of purposes. In TeX, there is a much more restricted approach to tables. Tables are famously complex beasts in the TeX world, and Knuth did point out that's it's amazing that they work at all! In most typeset documents, tables are used mainly for 'formal tables', and these have a pretty restricted range of 'good' appearances. As such, there is less need to provide the full range of CSS-like controls.
As canaaerus says in his answer, the TeX world is managed not by a committee but by no-one, and so what gets implemented depends on what individual users want. There are a range of table packages out there for LaTeX, plus the ConTeXt approach and the raw
\halign in plain TeX. However, they are mainly trying to solve other problems, which tells you where the priority for users is.
As a member of the LaTeX3 Project, I know that we certainly are discussing better separation of content and design. One issue that is worth bearing in mind here is that the HTML + CSS model does not always translate well into what we want for typesetting. There are some significant differences between the two areas, and that means it's never going to be as simple.
Any better approach has to work with TeX, both in code terms and for interface. We have experimental code to deal with the relationship between objects ('l3ldb'), plus the idea of 'templates' for design, both of which are in this area.