"if an employer wants to not hire you because of your race/gender/nationality etc, it can do it anyway in a later stage"

First, you're increasing the probability of discrimination by making it possible earlier on. The number of people that could exclude you goes up; e.g. the initial, possibly external, recruiter (who is screening hundreds of candidates) who would never otherwise have seen your face, can now discriminate on appearance.

Secondly, people are less discriminatory to people they've actually met and gotten to know somewhat. A picture of an anonymous person, with very little other information to go off of, may affect someone's judgement quite strongly; whereas, when you actually meet and talk with someone, have a lot of other information about them, and they are no longer anonymous, physical appearance will have less influence.

France tried the complete opposite (making resumes completely anonymous) and considered making that the law everywhere. When they tried it, it had the opposite effect of what they expected (hires became less diverse).

https://www.povertyactionlab.org/evaluation/discrimination-h...

"They also found that participating firms attached less importance to interrupted work histories or other negative signals for minority candidates. This suggests that anonymizing resumes may have made it more difficult for employers that were originally more favorable to minority candidates, to identify these candidates, and to assess their application in light of the adverse employment conditions many of them face."

That makes sense. It's sort of like how I wouldn't expect someone from Kentucky to have the same internship opportunities as someone from the bay area, but if I cant see their location then all I have to go off of is the listed experience.