Bad situation all around. Don't do it. She literally wants to have her cake and eat it too. I bet she wants FWBs, but wants YOU to remain focused on her. As in, she sleeps around, but you don't. Dealt with those before. They suggest that they want you to get with someone else, so that they don't have admit to liking you, or committing - while being able to act like they're single, and doing whatever they want. Then when you follow through with their suggestion - they come storming, calling you a player and liar and blah blah. Back and forth as it suits their interests. This is all about control. *****es like this are selfish and dysfunctional. Hence, wanting such a situation in the first place. All she wants is ****; probably lusts after and ****s hot bad boy types, isn't interested in nice guys who fall for her, etc. She probably KNOWS you like her, and is using it to her advantage.
This may sound extreme and bitter, but its a strong word of caution. Devious *****es do exist out there, and she doesn't sound too far off from one. Been in similar situations many times. She's basically saying you're only good enough to a certain point - ie, whenever she's horny, or wants something. You're a friend who gets sex. So, she's using you for everything + sex. You're still being used, and you must not succumb to this ****; thinking its all you're good for. Don't ask her why she doesn't want more, or what you could do differently, let her criticize you in any way, or follow along like a chump. Respect yourself more than this, and realize you can do much better - because you can. Don't let it take a hit to your self-esteem, 'cause she's not worth it.
Unless its mutual - even in an FWB situation - dont do it. Its never going to turn into more if she gets whatever she wants, and you get nothing (or next to it). Don't buy into the delusion that having a part of her is better than nothing. Don't view her as a good person who's just confused, and will come around once she finds out how great and wonderful you are. She already knows, and is trying to use you. This does not a good person make. She clearly doesn't care about YOUR feelings, so you should. All I hear is "she wants". If that doesn't match what you want (ie, mutuality) - **** her. Let her be selfish with everyone else she is playing. And, I bet you're not special here. Multiple FWBs and one-sided relationships are common with selfish types.
You also mention another "hope" you have. This is the wrong mindset. Don't do this (walk away) to make her want you more - do it to get rid of her. Don't try to win her over with crap games, or assume she is playing one. Get rid of her for you. You say what you want, but are thinking of following along with what she wants - despite coinciding with your desires. No good, sir.
At best, she will come back because she can't control the situation anymore. Similar to how girls as friends intentionally sabotage your relationships with other girls - after telling you to drop dead - only to act oblivious to their manipulation and control. ****'s real. Not just crazy talk, here.
You're gonna be torturing yourself if you go through with it. She won't commit, or stop seeing these guys. It's gonna be a rollercoaster full of mixed emotions. Not healthy or fun to be walking on eggshells, and trusting a selfish person with your heart. Bad news. She doesn't have your best interests in mind - only hers.
As much as it sucks and hurts - you have to get rid of her completely. For you. Start focusing on you. Stop making it all about them. And, if you think about it, with the mindset you have at the moment - you're both being devious and untruthful - especially if you follow through. Two crazy people who are using each other and playing games and trying to control the situations through manipulation is the worst way to start a relationship. This is a relationship based on lies, control, deceit, selfishness, etc. Horrible. Keep that in mind.