The house I am thinking of was built last year. I would have preferred the house have a heat pump underfloor heating system - They had a massive 20kw (72x280w panels) solar array and underfloor heating in a large concrete pad can stay warm for days.
Problem with the particular system was no dump load for excess solar once the batteries were full.
Hydro is still a problem as lake levels do indeed get low - until Tiwai point closes and there is grid capacity to redirect that power. Building new hydro is a problem with cultural and political barriers - In Hawkes bay the ruataniwha scheme was cancelled recently for those reasons.
Pumped hydro can also supply a dump load for oversupply and frequency correction without encouraging people to buy batteries / power walls for their houses which have the recycling issues. In Australia they have issues with over supply on the grid due to all the solar - a pumped hydro system could suck up a big amount of that excess.
Yes in the area to the south/west of lake taupo, because many of the consumers are seasonal, the lines company charges based on peak demand as they cant recover enough through a per-unit tariff to keep the network viable and fair for the all-year-round consumers. Its quite interesting when you look at the varied ways lines companies charge across NZ.