This is all dependent on the specific heater, instantaneous/continuous/on demand gas water heaters are widely used in Australia but they have closed loop regulation at the heater. When used with a controller to set the desired output temperature for each use there are no problems with stability other than low flow rates.
Yes, they are widely used in Spain too. They are the most used solution here. Some drawbacks I see:
Compared to tanks they are complicated, expensive to buy, expensive to repair and prone to needing repairs. To do all that regulation they have complex electronic systems that can break down and if you are lucky you can find a replacement board very expensively. If you are unlucky you need to replace the whole heater. OTOH, a water tank just sits there for decades and knows nothing about electronics or repairs.
On demand gas heaters can only modulate power within certain limits, say 35 or 40% at the lower limit and 100% at the upper limit. If it is going to actually modulate then you need your centerpoint to be, say between 50 and 80% of capacity, so you have range to move around. So, really, the modulation range is not that great.
Add to that the great variation in power needs and you can see an on-demand heater is just not suitable for many circumstances.
Assume in winter water arrives at 4ºC and you need 15 L/min at 74ºC.
Assume in summer water arrives at 24ºC and you need 3 L/min at 40ºC.
The ratio of power requirements is over 20 and no on-demand heater can do that or even come close while a tank can do that and more.
The combined heating and domestic water on-demand gas boilers we have here resort to different tricks and they kind of work but they are more inefficient than simpler solutions.
In summary, a complicated solution, expensive, prone to problems, inefficient, expensive to buy, expensive to run, expensive to maintain and repair.
These days we are having a heat wave in Europe and water is coming out of the faucet at over 25ºC. The minimum amount of heating my gas heater can provide is way over what I need for a shower so the only way to take a shower is to open another faucet and dump heated water into the drain while I shower. Not something I like to do. Maybe I can take a bath instead.
I understand the need for complicated solutions in a spacecraft where space is at a premium but I prefer not to spend hundreds or thousands of euros and endure crappy showers just to save a little space and have a nice heater hanging on the wall.
Yes, we have on demand gas heaters here. I don't like them. Personally, I prefer a tank any day but that's just me. Other people have other preferences.