If the bias is subconcious, moving to this would still have an effect.

People are remarkably good at picking up on subtle signals that correlate well with their existing biases. Instead of "It seems like a women" they'll subconsciously think "It seems like an even."

It wouldn't be perfect, but most of the effect would be removed.

In general, it could be enforced as a random identifier generated with each electronic application; this just burdens employers with implementing an electronic applications system, which is too high a regulatory burden (and would make dropping off a CV in person impossible/illegal, which is stupid.)

It could be a hash of the persons name, too, but then the public would have to learn what a hash was...

NI number works well in the UK, because it's convenient (and the original suggestion was specifically for the UK.) A similar system could be used anywhere.

"SSN equivalent in Poland has sex encoded"

That gets supplied when sending a resume?

It's not. OP wrote about using SSN-like numbers instead of names, so I wanted to note the fact that those number can, and quite often do, encode additional information.