The issue of finding a location that has dramatic elevation change, a basin capable of storing vast amounts of water, and a suitable source/sink for pumping make pumped hydro difficult to deploy. Then there are additional logistics challenges such as environmental damage and proximity to human settlements for maintenance and engineering teams (prior challenges mean you don't really get to select the locations).
Heat sinks meanwhile can be built wherever you have a big rock by drilling some holes. Additionally, gravity definitely does lose stored energy in its "stable state", through evaporation and water entering the water table. Losses depend on geology and local climate, but it's not negligible.
Not to say that pumped hydro is a bad technology, it's just got it's own challenges and uses. It's most applicable in the form of electrical grid storage. But specifically on the scale of keeping towns and cities warm, heatsinks outperform almost across the board.