Why wasn't \fbox defined to enclose its contents based on the most left, right, bottom, top parts of its contents?

Question

Case 1: \fbox cannot enclose characters tightly

Why don't \fbox and PSTricks \psframebox enclose its contents accurately? In my opinion, every edge should exactly touch the outer part of its contents. Does changing font solve this issue?

\documentclass{article}
\usepackage[english]{babel}
\usepackage{pstricks}

\fboxsep=0pt
\fboxrule=0.001pt

\begin{document}
\color{red}\fbox{\color{black}3}
\end{document}

This funny feature might be the source of problem where pdfcrop accidently trims grid labels.

Case 2: \fbox cannot enclose PSTricks grid labels

It is another example where \fbox and \psframebox cannot accurately enclose their contents.

\documentclass{article}
\usepackage[english]{babel}
\usepackage{pstricks}

\fboxsep=0pt
\fboxrule=0.001pt

\begin{document}

\color{red}
\fbox{\color{black}%
\pspicture[showgrid](3,3)
\endpspicture
}

\vspace{1cm}

\psframebox[framesep=0pt,linewidth=0.001pt,linecolor=red]{%
\pspicture[showgrid](3,3)
\endpspicture
}
\end{document}

Should the frames enclose the grid labels? In my mental model, they should.

Questions

In my mental model, \fbox should enclose its contents tightly when \fboxsep=0pt without allowing any part of its contents to reside outside its frame. If \fbox allows any part of its contents to live outside its frame, what is \fbox actually for?

Why wasn't \fbox defined to enclose its contents based on the most left, right, bottom, top parts? I think it is more useful, right?

Answer 1

the bounding box of the character has nothing to do with its contents:

\documentclass{article}
\usepackage[T1]{fontenc} 
\usepackage{mathpazo}
\begin{document}
\fontsize{3cm}{3.1cm}\selectfont\frame{\itshape ff}
\end{document}

Answer 2

TeX has no notion of how the ink will be used to draw a character. All it knows are the bounding boxes of characters, but typically a glyph is not entirely contained in the bounding box reserved for it. Letters with rounded shape at the top or at the bottom (the digit 3 is a prominent example) usually are drawn slighly over or under the bounding box, to align optically with one another. Often the "f", especially the italic shape, protrudes from its bounding box. It's impossible for TeX to know whether this happens or not.

However it's possible to access at the "real" bounding box of a character with XeTeX, as shown in XeTeX-reference, page 8. With TeX Live one can access to the document by texdoc xetex.