Note that your patch has a false positive with the empty string, which is
optimized to be always the same object (well, ISTR there are two, a unibyte
one and a multibyte one).

(byte-compile '(let ((x "")) (eq x "")))   =>   Warning: `eq' called with
literal string that may never match (arg 2)

(let ((x "")) (eq x "")) => t