We already use a mix of <cstdio> and stdio.h unconditionally throughout
the codebase.
Us checking this header also duplicates work already done by autotools.
Currently stdio.h is checked for 3 times during a ./configure run, after
this change, at least it's only twice.
We don't include strings.h anywhere.
This is also already checked for by autoconf, so us checking for it just
means a 3rd existence check during ./configure.