Instant on water heaters are an extremely common way of supplying hot water. They come in both gas and electric. They can be sized for a sink, like that one, or as a whole house unit. In modern US homes, they are often put in bathrooms/kitchens that are far away from the main gas water heater. This allows the user to get hot water pretty much immediately but still get most of their hot water from the less expensive gas unit. The unit will work until the hot water from the pipes warms up past some set point. They are also used in those cases where a room/area is added as an occasional guest house. This allows them to just run one water line (which may have to be drained in the winter, so one line can be better). I have seen the gas ones in homes in Poland and in pictures of homes elsewhere in Europe. They are usually placed on a wall that is common to both the kitchen and the bathroom to easily supply both.
Some of the advantages are that they are small and can be put almost anywhere as opposed to a large water tank. If the gas ones don't use a pilot light, they do not use energy when no one is using hot water (except maybe a transformer for the ignitor). The electric ones don't generally use any power unless needed. In countries with 220V electric supplies running a power line to the unit is easy (lower amps needed for 220V). The tank style water heaters lose energy all day. The tank style heaters can run out, but the instant on ones put out the same amount of hot water all day long. In old buildings, there may only be one water line going to a room, and this is an easy way to put hot water in a room. Also, as you found, you only really need to run one pipe to the shower also. More water, cooler, less water, warmer.
Some of the disadvantages of them are that they are more expensive than a typical water tank (assuming no additional water lines would need to be run). They will only heat up a certain amount of water a certain amount of degrees, so if you turn the water on too high, you are screwed. They require a rather high current to run, especially on 110V systems. They can get clogged up with deposits like a tank can, but will stop working when they do.
These are actually very similar to the electric shower heads.
I don't travel as much as you do, not even close. You go home almost as often as I travel. BUT I have seen these heaters a number of times, just never a single one in a room. They have always been bigger units outside the room someplace. I suspect, if you followed the water lines in hotels with hot water, you would see these more often. Look under the sink, in utility closets, etc.
I looked into these a couple of times and know people that have the larger gas units. The gas units that they sell in the US are rather expensive, and it does not look like energy savings alone would be a large driver. The heat lost from a tank heater is not sufficient to give a quick return, if any, on the high cost of an instant on. The smaller electric ones are fairly cheap, and if you use hot water only occasionally, don't need a high flow, and you have a large enough electric service, they can save you money in the long run. But I think the driving force behind getting these is not energy savings but rather, space, ease of install, ease of maintenance.
If you can stand the temps of the water coming out of the system, it is not really killing much for bacteria etc, BUT it does tend to make soap work better, and you are more likely to both take showers and take longer showers if they are warm and comfortable. The temps that a water heater tank is supposed to be at WILL kill many bacteria, the water temperature that we take showers in is a rather comfortable temp for Legionnaires disease amongst others. So, it is recommended not to turn your tank water heater down too much, even though it saves lots of energy. The lower temps don't affect an instant on, as the water is not hot long enough to encourage growth.
Here are a few more home made hot water supplies at thereifixedit.com
Two types, there is the shower head, very common and this more expensive type shown in the video. The shower head type cost about 15-20 dollars and this one cost about 50-100 dollars. The gas ones I seldom find, my friend in the Platypus Bogota in Colombia has a gas one, I do not know how much they cost, I do not see them.
90 percent of the planet uses 220, so easy outside..
Normally they do not make enough hot water, you have to take great care and adjust, they do not hide them in the under-developed world. 99 percent are in the shower with me, this one is unusual because it is better, bigger and does the sink also.
I would say extremely cheap in most countries to have this type, just not the USA.
They do not hide under sinks, they are not hidden, I know exactly where my hot water come from, I am an expert on this. More expensive hotel will sometime hide, or worst yet try to use one for two or three room, this is truly a jerk move. These things need to be seen by the person taking the shower to make sure they are:
1. Turned on.
2. The reset button is reset
3. The light comes on.
4. The water entering the device is turned on.
5. The breaker switches or fuses before the thing are turned on.