It's certainly non-conventional to charge for reference checks, and the balance of power isn't employee-favorable enough to do so in the general case. For junior roles, just give the "Classic 3" (three references you choose) and be done with it. Don't try to set it up as a consulting contract. You probably won't be dinged on references so there's no point.

It's more of an issue for upper-tier roles where reference checks are actually competitive-- i.e. turning up 6's and 7's means you don't get the job because they expect 9+, some of your references have to be supervisors/executives, and more than 3 plus back-channel are involved. That's when you should seriously consider charging. Hiding it in a PDF that no one reads is preferable.

Honestly, I'm inclined to give the "Classic 3" for free: 3 references that I pick to validate that I'm a capable person. I'm not going to play Internet Badass and claim that I charge for that; that's free. I know, at this stage in my career, that I'll usually get the job given that (if they really need 9.5+ level references and I can only give 9.0; then they weren't that into me to begin with). However, if they start to play "We need to speak to a supervisor" with me, then I start to charge because they're making me do above-board consulting work and I'm only willing to do that for free if I get the job.