there are however, decent people pushed to cheating by a very controlling partner.
No.. there are codependent people that are too addicted to the shitty life with their partner to leave so they cheat.
@ OP: The problem with chronic cheaters is that they are addicted to new relationship energy so once they and their primary partner's "NRE" wanes, the addicted go out and scout for a fix from someone else. These people should not be so sociopathic as to promise monogamy when they are incapable of remaining in that dynamic without therapy with a sex addiction counselor to help them change and give up their need for strange.
Your current girlfriend sounds like one of those that should refrain from committed relationships, or she should find someone who is like her and also needs strange and agrees to an open relationship because they are the same (not to settle) or she should get the sex addiction counselling it appears she may need.
Don't expect her to change for you or anyone else.
“The willingness to accept responsibility for one’s own life is the source from which self-respect springs.” ~Joan Didion