I am not an expert, so I am not familiar with the construction of this type of feature. Based on what you said you wont intentionally have a bunch of moss everywhere. That means you can power wash, bleach, etc to maintain and clean your features. That makes it not such a big deal in my opinion, and if the waterfall/weeping walls are circulating pool water then it will always (assuming you check it lol) have chlorine which will prevent most of the algae in the rocks right? The living moss idea just had images of hand picking leaves and gunk because you could use a power washer or chemicals without killing the moss. Since you aren't having actual moss, I wouldn't be afraid of it! I would loved to have built that, but there were not any qualified pool builders for something like that with in 100miles of me or I would have. Go For It!
We opted for stamped concrete around our pool just for ease of maintaining (and lack of qualified installers in my rural area), just food for thought. With that rock wall though, natural stone would be excellent as well. Ill try and get a pic up of mine for you.