I looked at top-fed wicking in my search to try to omit the water pump.
The wicking material has a very low lift, then gravity keeps pulling the water down the material, so it keeps wicking more out of the top reservoir as the top of the material losses its water due to gravity. If gravity pulls the water down the material faster than it evaporates, you'll need a collection reservoir at the bottom (it's not
limited, hence not
regulated, by the material being saturated by water, but by gravity). And you'll need to periodically move the water from the lower reservoir to the top reservoir. There is no way to regulate the water flow. If the rate of evaporation is greater than what the wicking and gravity feed provides, you'll have unconditioned air sneaking through.
I tested this and gravity emptied the upper reservoir out and I ended up with the material drying out from the top down. Fortunately, I was testing with the bottom of the material sitting in an empty sink with an open drain, so no flood.
You could automate the water return to the top with water level switches and switched pumps, but you've introduced several potential points of failure. A timed pump, duration and frequency, could be determined and setup, but if temperatures changed and your evaporation rate changed, your timing values could be out side of that required.
And as the air in the room/structure where the cooler sits gets more humid, cooling rate lowers, until it stops. You need something to let the humidity escape. As that moisture escape has to be at a fast enough rate just to have cooling, let alone maximize it, that will mean you have to exchange the air to provide dry enough air to get evaporative cooling. For cooling efficiency, you'll not be able to count on "ambient" wind for air exchange, so you'll need a fan. If you're going to need to use a fan anyway, then they can use your design or a variation there of and get hot dry air forced by fan to maximize evaporative cooling.
For your designs where water is continuously pumped to the top and runs down through the filter, both wetting and cleaning, there is no problem. With ample wet available, cooling is limited by fan, air temperature and humidity. Cooling on demand by switch.
With a wicking filter design sucking water up from a bottom reservoir (from theOtherDoc), it's self regulating as it can't suck up more than it can use. So as long as it can wick up enough to keep cooling the drawn air flow rate, it's good to go. He's apparently found components that don't draw more than the wicking rate can feed.
To scale up your design for their use:
It could be problematic to know, and before hitting the playa, when you have or haven't reached a design limit of the air-flow rate vs. filter kept wet. But, you know your existing box design with air coming through a larger area of filter (more usable filter compared to the bucket/pail version) works well, and how large a structure it cools, and how much power it uses. I suspect their reliable course is to make enough units of that design to provide the cooling they require, rather than rely upon a scaled up design that is not playa-tested and could have unforeseen factors involved?
They can also turn a number of units on/off as their cooling needs change through the day. Multiple thermostats at cascaded set points would automate this.