Water that's been sitting in a heater tank is oxygen-deprived and tastes dull when you use it for food preparation. That's the main reason to use aerated cold water instead of water from the hot-water system.
Probably because hot water is stored and if it happens to go below a certain temperature bacteria can multiply
In some houses, the hot water is fed by an open header tank in the ceiling. Whatever dust, dead mice or bird poos fall into that, can contaminate the tap water. I went off drinking hot water as a kid after seeing the deep layer of fine dust built up in the bottom of it.
As pointed out in a different comment thread here, that’s a header tank which was used in older, multi-level buildings where city water pressure was not adequate for the rise to upper floors. Builders would set up a tank that slowly filled using the lower pressure and could act as a sort of mini water tower for the building. This did not contain hot water, but there is a chance a hot water tank was using this supply.
Where I lived, the cold water was at much higher pressure than hot. I assumed it was common for cold to be mains pressure and hot to be from a header tank when present. Maybe it was an unusual case of retrofitted hot water (house was likely built before the invention of hot water).