Public information is not the same as public domain. They still hold the copyright on the streams, making reuploads illegal.
Also, aside from legality, it's simply morally wrong. They consented to be watched once live (or, if they enabled recordings, until they delete the VOD), not for it to be shared around on third party sites forever - regardless what Chaturbate put in their TOS to cover their asses.
Redistributing copyrighted material without permission is not only illegal when it's for profit. What you're alluding to is Fair Use (which does not require to be not-for-profit). And given the four factors of Fair Use, I think you're going to have a hard time arguing in court that uploading the full stream without adding anything constitutes Fair Use.
And I did not say it was not in public. But it was made public intended for one-time, live viewing; and not respecting that is immoral.