Private prisons don't make crimes in the sense of making people do things that are widely regarded as immoral, they just seek to make sure things already regarded as immoral become or remain illegal, and seek to have the penalties set as high as possible. That isn't what security companies would need to do to increase demand.

Remember that the costs to security companies of trying to increase crime rates would be born by whoever lobbies to reduce police effectiveness, whereas the benefits would be shared by every security company. Industries form associations to get around these problems, but you can only really do that if you can claim with a straight face that you're acting in the public interest. But while "We need to be tough on crime" and "I'm helping to keep criminals behind bars" are two statements that are easy to publicly resolve "We shouldn't waste so much money on police" and "You should give me money to protect you" make the speaker look like a hypocrite.

I'm sure that security companies lobby in various ways to get legal exemptions to weapons laws, let their employees detain people more easily, etc. Just probably not in ways that would increase crime.