Actually it has as much evidence as you have time. Take a big bag of fair dice, and split them randomly into two groups. Actually, split them however you want, whatever "lines of demarcation" you choose. Then roll them and apply literally any measure of literally any statistical outcome you want.
Oh shit, it turns out: in a just world, outcomes along arbitrary lines of demarcation are roughly even! Every time!
> Never has there ever been equal outcomes between any groups in history.
So? You need to assert that history has been just to different groups for this to be evidence to support your statement about what happens in a just world. Are you asserting that history has been just? Think hard before you answer this one.
> What leftists like to do is over-simplify the world to fit their pre-conceived notions.
Sure, like my dice example. Except the problem is, for my dice example to be wrong, you need to specify a reason why some dice roll differently than others, and you need to split the groups based on this reason. Remember: any arbitrary split must necessarily have roughly equal outcomes in a just world. If the world is just, any clear variance from equal outcomes must be due to some intrinsic differences in the dice themselves.
Let's say we split humans into two groups based on whether their birthday is an even or odd number (day of the month). This is a line of demarcation between groups of humans. Let's use your first sentence here:
> The very idea that, in a just world, outcomes along various lines of demarcation between groups of humans would be roughly even has zero evidence to support it.
So this is where we disagree, right? I assert that these two groups would have roughly the same outcome in almost any measure. It's a clearly arbitrary line. But you say there's no evidence to support that. Really? Really? Do you really believe that the odd-birthday group would be significantly different in outcome than the even-numbered, in any way? Of course not. In literally any "outcome" measure you could come up with, these two groups are indistinguishable.
Let's say we split humans into two groups based on biological sex. Would we expect to see any differences in any outcomes? Of course: there are differences in average height, muscle mass, sexual preferences, arrangement of sex organs, etc. There are actual intrinsic differences between these groups that account for some differences in outcomes, even in a just world.
Now let's say we split humans into two groups based on skin color. Uh-oh. We see huge differences in outcomes here. Can we explain it by intrinsic differences? Careful. There are really only two options here: either the world is not just, or skin color is not arbitrary. Asserting the second is literal racism: you're saying there's something naturally different about people with black skin that accounts for their vastly greater rates of poverty even in a just world. That's textbook racism, and, even worse, plain-old incorrect. It's also simply not logically necessary, because we know the world has not been just. Very, very not-just to that particular group, in fact.
> If there is racial disparity, it must have been caused by systemic racism!
Such a vapid strawman argument. This bullshit only works if we've never actually observed systemic racism. Slavery, the Greenwood bombing, segregation, Jim Crow, police slayings -- those are not hypothetical events dreamed up by "leftists" to account for racial disparity we observe. Systemic racism did happen, and in many cases is still happening, and then later we observe that there is also racial disparity. These "leftists" go "hey, maybe the racial disparity we see now has something to do with all that systemic racism that was going on for hundreds of years" and you pretend like this is some unfounded conclusion-jumping?
Your train of pseudo-reasoning, like that of so many other racism-apologists, only works if you conveniently ignore the actual multi-hundred year history of actual racism that actually happened. So many of your points sound completely asinine when you re-read them with that in mind.