To start with, randomly generated usernames weren't mentioned, and they are not a prerequisite.
> It "generally" doesn't, because the average user isn't randomly generating usernames per-site
What other people do, whether average users or not, doesn't matter. When average user Alice is registering accounts on Websites A and B, the fact that average user Bob doesn't use different usernames for his accounts doesn't change the fact that if Alice would have otherwise registered account agirl on one site and pie_maker26 on the other, but instead has been forced to enter her email address, then that has a non-zero effect on risk.
For the claim as stated to be untrue, the difference in risk would need to be zero.* But it isn't zero. The claim as stated is true.
> For it to practically make a difference, you'd need someone who cares about […]
That's not true. Users who are exposed to lower risk by accident are still exposed to lower risk. It's not a prerequisite for the user to care at all, nor does it require them to understand any of this or to be trying to adhere to any particular scheme to achieve a certain outcome. The only thing that matters is what they're doing—and whether what they're doing increases or decreases risk. Intent doesn't matter.
* or it would need to be somehow less risky when email addresses are required in place of where a username otherwise would be, but that's not the case, either