People tend to refer their friends. Even if you're not friends outside of work, you're more likely to refer people you were friendly with at work.

Sure. And most of that happens in the context of "refer anyone and we will vet them with our hiring process". If you change that to "only refer people whom you personally vouch for because we will trust your judgment to replace parts of the hiring process", there will (or can) be incentives to refer people who are really good, not just people you personally like and would like to help out. If you combine that with hiring people who've worked in diverse environments, that might counteract the natural referral biases.

That's a good point, the demographics of my coworkers are nothing like the demographics of my friends. Most people are probably more likely to refer people who are both friends and coworkers though.

But a monetary incentive based on performance might be able to change that.