The crux of the issue still remains the equality of outcome vs equality of opportunity. Nobody expects an equality of outcome (we are both in agreement here); where we differ is on the equality of opportunity.
If the playing field is not level, there's no basis to talk about purely judging singers when they sing. If so, all the greater is the urgency in dismantling/reforming the system.
In the context you cited, there's no discrimination in the equality of opportunity.
As a singer , like you alluded to the type of song you use can have different result.
You want to judge them all by singing the same song at the same time here. Do you think you can find the best singer this way?
We have a world today that is not fair. In a singing competition , every singer will not have the same level of coaching or same type of voice or some type of expression etc etc
One singer will sing first while one might sing it last.
Does the one who sing first has an advantage or the one who sing last has an advantage?