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.