Simply speaking, I want my toolchain to intrinsically know where to look for (system) header files and libraries — in $PREFIX/include and $PREFIX/lib respectively — so that when I set CC=$PREFIX/bin/i686-gnu-gcc the right directories are picked up automatically, just like the system compiler picks up /usr/include and /usr/lib without me having to add them explicitly.
That doesn't sound like a very strange thing to want, does it?