However, it is simply not true that hydro-pump storage never has a dam.
See: https://en.wikipedia.org/wiki/Pumped-storage_hydroelectricit...
https://en.wikipedia.org/wiki/Ffestiniog_Power_Station
In fact, when you look at the list of pumped storage stations, the vast majority of them have dams:
https://en.wikipedia.org/wiki/List_of_pumped-storage_hydroel...