Without cultures you don't have UU's

That is the point. In C2C you have to develop your culture in the same way as you have to develop everything else. Admittedly we have only gone about half way to a full cultural development system. A full system would see all of the current cultures (and religions) gone.
Without assimilation on you don't get the base culture of the conquered city. Very important if you want to build the cultures belonging to that base culture.