They are most certainly not unique to less developed countries. Electric showers are quite common in the United Kingdom and Republic of Ireland. They're typically used for energy-efficiency purposes as they only consume power while in use, rather than heating a large tank of water.
There is certainly no issue in these countries with instability of power supplies or anything like that. It's just a simple environmental/cost saving measure.
The UK/Ireland system is quite different from the models described here. They are usually a small wall-mounted control unit which can be rated up to 19kW!
They are also installed to a very high degree of electrical safety and well regulated standards are applied.
They're very effective, and do save quite a lot of energy, particularly during the summer months when central heating systems may not be in use.
It's also quite common in much of Europe to use instantaneous gas-fired water heaters. These start heating the water as soon as a tap / shower is turned on and stop when it's switched off again.
These may form part of a 'combi' boiler (furnace) which has a separate system for heating radiators in the building.