`quit_char', `set-quit-char', and `set-input-mode'

[Drew Adams]

* Variable `quit-char' is only in the C code. There is no such Lisp variable.

* Function `set-quit-char' exists, but is not even mentioned in the Elisp
manual.

* Function `set-input-mode' is mentioned in the manual, but it just seems more
roundabout than `set-quit-char'.

Why isn't `set-quit-char' documented as the way to set the quit character?  Is
there some advantage to using `set-input-mode' for this?
 
Why don't we have a Lisp variable for this (even a user option perhaps)?  Why
must we use special functions to set this character, rather than just using
`set' with a variable?
 
If we had a variable, then code could check whether some event was equal to the
quit character, instead of checking only the hard-coded value 7 (C-g).  If
something changes the `quit_char' from C-g to something else, then code testing
7 will no longer DTRT, no?
 
I'm guessing there are good reasons for some or all of these things - reasons
that would help me understand better. Explanation appreciated.