Why does cmsy10.tfm give the minus sign a positive depth?

Here's one of the reasons why the minus sign has the same height and depth of the plus sign.

\def\nodepthminus{\mathbin{\setbox0=\hbox{$-$}\dp0=0pt\box0}}
\def\noheightminus{%
  \mathbin{%
    \setbox0=\hbox{$-$}%
    \dimen0=\fontdimen22\textfont2
    \advance\dimen0 0.4pt
    \ht0=\dimen0
    \dp0=0pt
    \box0
  }%
}

\setbox0=\hbox{$\displaystyle\sqrt{a+b}$}
\dimen0=\dp0 \advance\dimen0 0.1pt
\def\guide#1{%
  \setbox0=\hbox{$\displaystyle\sqrt{#1}$}
  \dimen0=\dp0 \advance\dimen0 0.1pt
  \hbox to0pt{\vrule width 2in height -\the\dp0 depth \the\dimen0 \hss}%
}

$$
\guide{a+c}\sqrt{a+c}\sqrt{a-c} \sqrt{a\nodepthminus c}\sqrt{a+c}
$$

$$
\guide{+}\sqrt{+}\sqrt{-} \sqrt{\nodepthminus}\sqrt{+}
$$

$$
\guide{+}\sqrt{+}\sqrt{-} \sqrt{\noheightminus}\sqrt{+}
$$

\bye

The difference is tiny, but noticeable.

I have not checked, but AFAIR the bounding box for the minus sign is the same as for the plus sign. This makes sure that expressions like $x-z$ and $x+z$ are equally aligned.