I agree about the question on how effective it actually is
I actually prefer things not built into the vehicle as I like to take different vehicles depending on the trip. Or use around the house somehow if needed. I'd run this thing off a jumper pack, which I already carry anyway. I carry it because my power needs are quite low and I didn't want to build house batteries into my vehicles either. A jumper pack is dead simple, multi-purpose and can be used in whatever vehicle you happen to be driving. I personally prefer adaptable, multi-use systems. Which is why I also like the idea of shade cloth. Take it camping with whatever vehicle you happen to bring and use it to better keep everything out of the sun (coolers, interior, water, people etc.) not just the dogs. Meanwhile use it at home for a summer BBQ.
I was thinking of the swamp cooler as an ancillary system and the questions you pose are why I was interested in more feedback from someone who used it.
Can't say I'd, personally, be too worried about dog proof as my dogs usually just sleep while I'm gone, I tire them out. The site gives guidelines on power usage AND water usage. There are different models for with different reservoirs and also the ability to add a reserve jug on top. I'm always carrying water as it is. These DO NOT require ice. That would defeat the purpose.
Also I'd use it as a redundant system. Keeping them in a place, well ventilated, shaded etc. that would be "safe" without the swampy. With the swampy providing extra cooling to keep them more comfortable (and my mind more comfortable), as opposed to simply safe. You can use something like this with windows open, in fact, it requires windows to be partially open.
I think a roof vent/fan is a great idea too.