I watched a video that uses gravity to boil water just by lifting it and lowering the pressure. explanation is better in this video
https://www.youtube.com/watch?v=hHNoHhbfFDQ
so I’m running the scenario through my head of lifting the bottle to the point of “cold” boil then lowering it down (while keeping the hose above boil level to avoid contamination from the original) and I’m trying to figure out what the issue would be.
would the water vapor never condense until a temperature change happened, would it be too slow at distilling since there can only be as much water vapor can only be as much as the container?
what are the flaws or limitations
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I’m writing only based on your text, not the video, please excuse any doubling of content.
It is easier explained if you build an imaginary machine instead of lifting / lowering that does the same thing. The single most important thing to understand is that the lower the pressure the less heat you need to add to boil something. There are funny graphs for each liquid (for example https://courses.lumenlearning.com/umes-cheminter/chapter/vapor-pressure-curves/ ).
The intro explanation
The water in your containers will behave based on their individual combination of pressure and temperature. I’d at any point the water vapor falls below its boiling point at the current pressure it starts to form a liquid. At this point you’ve made a fancy rain machine.
Note that water itself adds pressure to a system because of its volume even as a gas
A machine
Imagine you have a container at 100 mmHg which according to a random online calculator leads to a boiling temperature of 50 degrees C.
Now you heat this up and lead the water vapor into another chamber which has only s pressure of 10 mmHg. Water has a boiling temperature of only a bit over 10C there! So you keep it at 20C to be sure the water never gets liquid again.
But wait: now you’re adding water vapor into a low pressure container - you’re literally pressing a gas into it - so you increase the pressure in there.
The first container, the source of the gas, becomes irrelevant: As soon as the additional water increases the pressure to around 20mmHg it starts condensation again as now it’s boiling point moved above the 20 degrees.
The flaws
As you’ve asked for the downsides: it’s a very convoluted way of manipulating water to achieve the same result as simply heating it. You would need way more energy to lift the containers far enough or otherwise decrease the pressure than the energy needed to boil it.
Other than energy and logistics I don’t see a downside. Liquids don’t behave differently in terms of boiling no matter the source: pressure, temperature or a combination.