Only some of the built tools are installed into the $tooldir: https://sourceware.org/git/?p=binutils-gdb.git;a=blob;f=binutils/Makefile.am;hb=d8bbdb9dd5653716b0f904bba69ca5b63acaca2d#l111 Most notably, "size" is omitted, but also addr2line, elfedit, gprof and strings. Whats the rationale which program also gets the symlink in the $tooldir, and which is only installed into $bindir?
Those are the tools needed by gcc or gdb, see ACX_CHECK_INSTALLED_TARGET_TOOL in the toplevel configure.