A bit of an elaboration on why water towers are used in combination with pumps. Pumps are great for moving a constant amount of water around at whatever rate the pump is designed for (e.g. a small pump will move something like 1 gallon per minute). a big enough pump (or series of smaller pumps) can cause that pumped water to consistently flow at that rate.

The problem is that people don't use water at a constant rate. In the morning, several residents probably all run the shower at the same time. if too many people open the water tap at the same time, a pump will give each just a fraction of what they expect.

But a water tank high up supplies water by gravity, you could open a large number of water taps, and as long as the pipes from the tank are big enough they'd all have the same pressure as if just one opened.

The water is gradually pumped up to the tank no matter if people are using it or not, then when many people want water, they all get it at expected pressures and the tank start to empty. Eventually people close the taps, the tank will slowly start to fill again from the pump.

This same basic design is also how water towers supply water to many single story buildings, it's not a unique engineering feat for skyscrapers, but an adjustment to fit somewhere within the building's footprint.

And water towers are still used to manage water pressure demands in municipalities.

Back when I lived around the 30th floor, I would turn on the tap and then wait 10 minutes for the hot water to arrive.

The trick was to wait until the people above you were having a shower, then it would already be hot.