Fine, if you are only looking at water side deltaT. What about your system deltaT?
When your 65F circulating air enters a room intended to be kept at 70F, it will take a lot more mixing/circulating to cool the room, since the TOTAL delta-T is only 5F. Air entering the room at 55F can do the job more quickly, with less circulation. Add outside air to the calculation? Or is that the "end of the story"?
The real uh is your tacit assumption in your first post that changing a setpoint will reduce power; that is only true, as you mentioned rather glibly, if the coils are grossly oversized for the original application, and thus have ample margin to handle the load at 1/3 of the original water-to-air delta.
It's possible that the approach can work in a scenario with less than design cooling load, but it's easier just to throttle back the flow and leave the setpoint alone, and probably works out cheaper on power, depending on the system design.
Bottom line - a chilled water system and chiller designed and optmized for one setpoint will not necessarily perform more efficiently by just changing the setpoint; often such "simple" approaches end up costing more (more pumping, more air side circulation, chillers operating off-design at lower efficiency).
Uh.