I got my graduate student to stop sending me documents in MS Word, and start using LaTeX, but my objection to Word didn't get to the heart of the problem. Of course, mathematical expressions look bad in a Word document, and the typesetting in generally worse in other respects, but it would be wrong to focus solely on appearance.
The rationale for LaTeX is analogous to a common cliché about the use of Latin, which is that Latin supposedly lets one express things very precisely. One thinks of old-fashioned lawyers making that observation to justify their use of Latin tags, although I don't know enough Latin to say whether that is valid. But, in the context of mathematics and science, MS Word provides a kind of license for sloppiness that is denied by LaTeX. Symbols, especially when the have superscripts, primes, and similar embellishments, do not get a consistent appearance in Word. Extra space amy appear before a superscript, or sometimes the font size changes, because the author doesn't have enough control. In LaTeX, any symbol has a corresponding sequence of ASCII characters in the source file, and there is no ambiguity about whether two symbols are the same, or different. Furthermore, features like the "theorem" and "proof" environments force us to state our theorems and proofs in a self-contained way, rather than having discursive paragraphs that segue vaguely into something that could possibly be interpreted as a theorem statement.
LaTeX, like Latin, does not prevent one from writing down a statement that is incorrect. (A widely cited example is "Dulce et decorum est pro patria mori.") But it does help to prevent vagueness.
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