In a terminal, one cannot distinguish Ctrl+A and Ctrl+Shift+A as they both emit the same key code, so I can see why Vim can't do it. But gVim, being an X application, can differentiate Ctrl+A and Ctrl+Shift+A. Is there any way to map those two things differently?
For starters, I'd like to do something like the following: Make "paste from clipboard" work like Gnome terminal, while keeping Ctrl+V to the visual mode.
:nmap <C-S-V> "+gP
Gvim doesn't do it because vim cannot do it (under normal circumstances). Sorry, but that's just how it is.
However...
Some terminals (e.g., xterm and iterm2) can be configured to send an arbitrary escape sequence for any combination of keys.
For example, add the following to .Xresources for xterm to send <Esc>[65;5u for CtrlShiftA. You can then map that in Vim to <C-S-a>. (65 is the decimal Unicode value for shift-a and 5 is the bit for the ctrl modifier. The u in this case stands for "unicode".)
! .Xresources
XTerm*vt100.translations: #override Ctrl ~Meta Shift <Key>a: string(0x1b) string("[65;5u")
iTerm and [u]rxvt can also be configured to do this (examples not provided).
More info: http://www.leonerd.org.uk/hacks/fixterms/