But LaTeX does use math fonts with mathematical symbols. But just using math fonts isn't enough to typeset math.
The other answer talks about 200-400 characters. LaTeX easily needs more.
For instance, there's a package to use Times and matching math fonts: its glyph table lists around 8 * 128 glyphs for math support (not counting the "used with the varg option", and ignoring that
txexa has in fact less characters):
That does not count bold math fonts, which is used a lot in your example.
But to typeset math, you also need to get right the vertical and horizontal positions of each character. For instance, not all superscripts have the same height — they must be moved according to the formula they are a superscript of. So you can't just use a raised 2 to typeset
$x^2$ (x square), as you seem to suggest. To know what's the formula you are superscripting, you need semantic markup, which seems too complicated to handle for even modern fonts technologies (though I'm not an OTF expert).
Big parentheses are another issue: a few sizes are drawn by hand, bigger ones are composed out of different characters (with matching vertical lines that can be extended indefinitely).
Donald Knuth's book about TeX (the TeXbook) spends 5 chapters (out of 26) on the rules used by TeX to typeset math, and on a few ways to override the defaults when needed. LaTeX and a few LaTeX packages add more rules.