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Look at the difficulty that S-Polynomial caused. How can anybody possibly claim the LaTeX allows one to concentrate on the meaning and not the layout? So LaTeX fails by its own criteria.
Well, from what I can tell it caused few difficulties that would not have been quickly solved (with a quick dip into the documentation). I'm much more fond of systems that allow me to fix difficulties once for many examples, than systems that force me to fix problems each time they happen to occur in my page layout.
I would have to say that for the genre it was designed for, yes, LaTeX does allow one to concentrate on meaning as opposed to layout to a greater degree than most of the alternatives. All I have to do is say that my document is an APA submission, a fiction draft, or a letter, and the rest of the styles happen naturally. With Word or with Open Office.org, I'm almost always forced to waste a lot of time redefining styles, and then I have no idea as to whether those styles will be applied consistently, or whether I might have to deal with "side effects" because that table cell was auto-formatted into a different style.
Meanwhile, there are other features that more than make up for the little quirks. Indexing, intelligent cross-references, and BibTeX are three must-have features.
Now, granted I wouldn't be using LaTeX for the types of output that would require something like Quark or Scribus, but I'm not paid to twiddle flowing text around artwork in variable collumn layouts. I'm paid to deliver thousands of words of double-spaced copy typeset just so with accurate citations, and images on separate numbered pages at the back of the manuscript.