Just because something seems like should work doesn't mean it will. Air conditioners are simple and cheap to install. An insulated swimming pool in the basement is not.
1 cubic meters of water chilled 10C below ambient is 40MegaJoules of energy.
Or in other words: 11kW-hrs of cooling, comparable to an entire Tesla Powerwall.
We aren't talking about entire swimming pools here. Just a few cubic meters of water. Shift the temperature delta as you see fit but... It's actually very space efficient.
Air conditioners have a COP of about 3 though. So really its more like 3.5kwh of storage. If you want to go lower temperature to store more then your COP drops.
Typical residential air conditioning is using 4kW of power. So your 40MJ of energy would be used up in 40MJ/4kW=10000 seconds, or just 3 hours. And its only theoretical, because it assumes 100% efficiency in storage and conversion
> Air conditioners are simple and cheap to install
Today. In my chats with the sort of home improvement types that seem to be in this thread, we're less concerned with today and more concerned with the cost of things in the future, as societies include "climate taxes" (in the form of actual taxes, subsidies, or whatever else) in the cost of things.