It's not overhead, it's about dependency breaking. 32-bit xors on a single register are universally recognized as a zeroing idiom, which means the CPU doesn't have to wait for the results of previous operations in order to set the value of the applicable register to zero.
In modern CPUs zero'ing idioms aren't even executed, they only get as far as the register allocater. The register allocater will allocate a zero'd physical register for the architectural register that had the idiom applied to it and the job is done.
In modern CPUs zero'ing idioms aren't even executed, they only get as far as the register allocater. The register allocater will allocate a zero'd physical register for the architectural register that had the idiom applied to it and the job is done.