Where does it say that it will specifically can not reduce the number of Persistent Contrails? As far as I can see from what you have posted the actual effects on contrails are not specified.
I would have though that more moisture in the upper troposphere would lead to at least larger volumes of ice-supersaturated air, and hence slightly more contrails, not just thicker contrails.
I would have thought that as well . . . however, I think the point is because of global warming the warmer temperatures reaching higher into the troposphere reduces or shrinks the optimal air potential to produce supersaturated air for ice more than the increased humidity would increase the potential for supersaturated air . . . so increased temperatures at altitude wins over more humidity . . .
That depends on the frequency of flights through various altitudes.