Well, not all demons. Just ones who were human and got turned.
And, well... I don't know about them wanting to stay evil. In a lot of cases, it's like your crossroads demon thing. The human made a deal for power for some reason or another, and now they have to lose their soul in the process. But, if caught at the right time, and if our version of the crossroads demon is vanquished, than the human can be saved without having to vanquish them, too.
For instance, we came across a human who was facing his final test to become a demon, so he wasn't a full demon, yet. And he had become a demon because of debt, really. He was in a lot of trouble from gambling, and a demon offered to pay off his debts if he agreed to turn. But, we were able to stop it from happening. He didn't want to be a demon, but he felt like he had no other choice when the offer came to him.