Why can't solar stills convert sea water into fresh water?

This technique is for survival only, not long term water availability. Solar distillation though doable requires Hours of solar exposure to produce barely a liter or two of water per day. Example: A typical swimming pool loses an 0.25 inches of water a day to evaporation or 0.15 gallons a day per square foot of pool surface (2.5 cups) Not much to go by if you're looking for liters of water. A children sized kiddie pool would produce 3 gallons per day if you could collect it using the same still method

I think this is one of the "gaping holes" you are looking for:

The amount of Total Dissolved Solids (TDS) in sea water is about 40,000ppm. Thus for every 1,000L of sea water distilled, you would have 40L of solids left behind after distillation. The amount of room left for water (i.e. the capacity of the 'hole') would thus decrease by 4% each time it was used. The 'hole' would be 50% full of solids after only 17 uses and 90% full after 56 uses.

Assuming you designed your system to go through one distillation cycle every day, your holes would no longer be viable — and would need to be abandoned — roughly every two months.

To rub salt into the wound, you would leave behind hypersaline pits that would kill virtually all nearby plant life. As you dug more and more pits along the countryside, you would progressively turn the environment into a barren wasteland, devoid of life, and subject to extreme erosion.

In conclusion, the illustrated design degrades quickly, scales poorly, and has grave, long-term environmental consequences. That's why a solar sea water still could be suitable for infrequent, individual use, but would be unsuitable for long-term provision of water to the public.

A solar still CAN convert sea water to potable water. They are commonly included in lifeboat kits. Check the Watercone or this survival guide.

In effect, nature does this already. The sun heats up a patch of ocean, water evaporates and rises into the atmosphere. The vapour then condenses on airborne aerosols to form clouds which are then moved by winds and given the correct atmospheric conditions, rain falls.

To produce significant amounts of water from a solar still would require either an extremely large region of ocean be covered with a condensing medium (such as a plastic sheet) or the area of ocean be covered with an extremely large number of smaller stills.

The other significant problem with this is the distribution system required to get the water from the one large still or the large number of smaller stills to where it would be required.

Other problems would be: what effect all this would have on the ocean environment and wildlife? What happens if whales, sharks, seals, birds, or other wildlife damages the stills? How do you prevent the accumulation of barnacles on the solar stills? How can the still be protected against the forces of nature, such as: wave action, winds, hurricanes and solar damage?

Then there is the economic question who is going to pay for such a system and how much will it cost? Are there cheaper alternatives and ones that are less problematic and less risky? How often would the still need to be replaced because of damage, exposure or wear-and-tear and how much is that going to cost?