I ask for three references if you're not P411. I do this because Gina over at P411 has your info so I feel safer and count her as a reference (and then require two references plus your P411 account.)
The thing about requiring three or more references is that a lot of references don't get back to us, or they take forever. Asking for multiple references means that you have a better shot of hearing from 2 or 3 in a day or two (sometimes less, sometimes more.)
I just finished with Phoenix and it was pretty reference-user unfriendly. The women who did respond were great. But there were just a lot of women who didn't respond, or who responded but were weird and didn't want to give a reference. I do not want to start collecting more conventional information (work info, ID stuff) because it's intrusive, but it's also more work than I want to do.
BUT, if your references aren't reference-friendly-- we're both stuck. That's why multiple providers, having an organized list to send out with dates and little pieces of trivia about your time with the woman so they remember you and can give you a good reference, is so useful.
But then again, you could also get P411.
If there are "far too many ladies" you can see with a few short emails and a simple phone call, then I don't get the vent. If you have a plethora of ladies you WANT to see who are so easy to see, then the other women who screen more thoroughly are kind of a moot point, don't you think? And if there's women you really want to see, then the best thing to do is make sure your references ARE going to give references when asked (asking them "can I use you as a reference?" is a first step) and then your 3+ references should speak for you.
I kind of half agree with your post and disagree with the other half. Luckily, you have a bunch of reviews so women should be able to go through your review list and use that similarly to a P411 okay list.