Interesting topic. I've been on both ends as I've foaled out a handful of mares for others (about 5 or so I'd say) and I've also sent a mare away so someone else could do it for me.
I can certainly see the plus side for the mare owner. If they can't be there 24/7 (which it what it really requires) then sending the mare out is a great idea. But before I'm going to send my mare somewhere I've got to KNOW how she will be cared for. References won't really help me too much in that I still can't see it for myself. I would want the farm to have online cams that I, and my friends, could watch and be able to see how the person handles the foaling process. And I would watch those cams before sending a mare of my own there. The barn has got to be in very good condition and very safe. Same for the turnouts. And the contract would need to state everything. What happens if the foal dies, what happens if nobody is there when the times comes, what kind of meds will be administered, what is the vet like (biggie for me!) and how close is the vet, what if two mares are foaling at once, etc. And then, at least in my case, if the mare is insured, the insurance company may want to have a say in where the horse is sent.
From doing it myself...it's a TON of work. It's stressful. It's heartbreaking when something goes wrong. You WILL lose friends, no matter how hard everyone tries to not let that happen. And it's not worth the money, imo. I believe (can't remember for sure) I charged somewhere between $250 and $300 plus monthly mare care.
Just be careful and go into it with your eyes wide open. And you must have help. One person can't be awake 24/7 for days, or weeks, on end.