Given the agricultural issues in that movie, perhaps the purification device was intended more to collect and concentrate the urea than to purify the water.
But that assumes the scriptwriter would have thought of that, which may be a stretch, given that Earth has insufficient water to cover all landmasses to a depth of 7 km. That would require about 3.6 billion cubic kilometers more water than already exists in the oceans, and there are only about 1.4 billion cubic kilometers of water on Earth to begin with, . Certainly there isn't that much locked up in glacial ice. That is only 26.5 million km^3, which is enough to raise sea level by a maximum of 52 m, far short of the 8 km it would take to cover everything but Mt. Everest.
Anyone who would skip that bar-napkin math was probably only putting that scene in specifically for the gross-out factor. It's just like Mad Max eating the can of dog food. Which is an apples-to-apples comparison, because Waterworld was written specifically to be an ersatz Mad Max.
IIRC the movie explicitly says "due to global warming" at the start or something to that effect.
But on the other hand, society had collapsed along with most of the stored knowledge of the world, so maybe it was just the people being uneducated and highly insular. They don't even know how long a kilometer is anymore.
There was a point in history a few hundred million years ago where the entire American midwest was a shallow water ocean; we could easily be heading back to that scenario in just a few centuries.
The era of the movie is 2500 AD. To add nearly 3 oceans worth of water in that time frame by cometary bombardment would boil the existing ocean.
The only hard sci-fi explanation is that someone towed Europa to Earth and slowly lowered it down via a cable or pipe. Terraforming by an alien aquatic species. Hyperintelligent space whales.
On a long enough timeline, especially with more energetic atmospheric conditions, isn't it possible for the land to redistribute itself more uniformly from the various forms of erosion to the extent that it's all submerged?
But that assumes the scriptwriter would have thought of that, which may be a stretch, given that Earth has insufficient water to cover all landmasses to a depth of 7 km. That would require about 3.6 billion cubic kilometers more water than already exists in the oceans, and there are only about 1.4 billion cubic kilometers of water on Earth to begin with, . Certainly there isn't that much locked up in glacial ice. That is only 26.5 million km^3, which is enough to raise sea level by a maximum of 52 m, far short of the 8 km it would take to cover everything but Mt. Everest.
Anyone who would skip that bar-napkin math was probably only putting that scene in specifically for the gross-out factor. It's just like Mad Max eating the can of dog food. Which is an apples-to-apples comparison, because Waterworld was written specifically to be an ersatz Mad Max.