Here is the design of prototype:
> A circular polyurethane foam (36 mm diameter and 25 mm thickness) was used as the floating thermal insulation. An insulating ring (36 mm external diameter, 31 mm internal diameter, and 6 mm height) made of polystyrene foam was attached on top of the floating thermal insulation. Black paint (245198, Rust-Oleum) was uniformly sprayed on the top of the thermal insulation layer, creating a 31 mm diameter area for solar absorption. Five 2.5 mm diameter macrochannels were drilled through the thermal insulation using waterjet. One of five macrochannels was in the center of the floating thermal insulation, while the other four were in four vertices of a square, 9 mm away from the central macrochannel. A circular copper plate (36 mm diameter) was used as the balancing weight, which was attached to the bottom of the floating thermal insulation. Similar to the floating thermal insulation, five 2.5 mm diameter macrochannels were also machined through the copper plate using waterjet. The total weight of the copper plate was 23.4 g to enable the neutral buoyancy of the entire structure. The convection cover comprised two glass slides (45 mm diameter and 2 mm thickness) and an air gap (5 mm thickness). The solar absorber for the contactless mode was a double-sided black-painted aluminum plate, attaching to the back side of the convection cover.
The $4 estimate comes from replacing copper with something cheaper.
Once the water evaporates, you can probably just condense it via standard methods that are both passive, and extremely efficient. So they don't bother doing it. Basically, this thing will be surrounded by some apparatus that collects the vapor.
These are tiny little things, less than 4cm in diameter and floating on seawater. They rely on the sun shining on them to vaporize the water, and in fact the linked paper says that the convection cover is needed when outdoors in the wind.
So... it implies that you can't have anything blocking the sun from fully shining on it, because it already has enough problems gathering enough heat when the wind blows, right?
Where does this condenser go? Obviously, I don't know anything about engineering in this domain ;)
For a family of 4, you need maybe 3 liters * 4 = 12 liters in a day. So you need a 3 m^2 device to satisfy them. Or something on that order.
Finally, this thing will probably be encased in a glass chamber, which will collect the water vapor and then condense them in some container. So that is a whole other additional cost. So, yes some sunlight will be blocked or reflected by this additional structure.
If you do a quick image search of "solar desalinator" you will see plenty of examples of how this condensation works.