Reddit mentions of Wind & Weather Indoor/Outdoor River Rock Floor Mat, 19-1/2''H x 30''W

So essentially...this bathroom will be less functional than a real bathroom (can't do anything "too messy"), require major upkeep if you do ever use it for normal showering (how you planning on dealing with conditioner build-up on many porous surfaces?), and cost a few grand to put in while reducing resale value of the house/requiring replacement before sale because no one else would want to maintain it.

It's an art project. If you want to pursue it for aesthetic value, and if you have the money lying around (between labor and materials...yikes. How are you planning on getting both concrete and rocks up the stairs, since you basically have two floorings? Are you sure the floor doesn't need to be reinforced?)...go for it, express yourself, this is your home and you own it for a reason. Customize. Go nuts. This is pretty doable, and there are even "compromises" you could make to make it more functional.

Look around at options, since you're not the first person to crave a river rock/natural bathroom unfettered by silly things like a shower enclosure. Consider slate bathrooms, concrete or concrete-and-bamboo combos, loose stones for only part of the flooring or in lower-traffic areas, traditional pebble or river rock tiles that you grout in, river rock with epoxy, river rock granite, enclosing the rocks in some way, or even river rock rugs or bath mats you can just haul up and down the stairs to hose off. Also think about other natural finishes like wooden/bamboo bath flooring, which will be less heavy and maybe could evoke a similar ~natural aesthetic~ for a little less money and effort.