i can't think of a reason for not using stone and unlike wood mulch it can't be wind blown nor carried by heavy rain into pool.

We used them on two sides of our pool (against the edges of the retaining wall), and used round river rocks, with a few small boulders. We are in GA, and it does collect pine straw and leaves, which are not easy to get out with the blower. But then we do have a lot of trees.

Also, dirt/debris does get below and in between the rocks and weeds do sprout, so it is definitely not maintenance free. We had heard that you could just blow-torch the weeds (won't harm the rocks), but tried that and it doesn't really work.

I don't have any close-up pix, but you can see the stones in this pic against the fence.

I think it would be fine as long as you'll be happy with the maintenance. For me personally, it's easier to weed mulch than rocks because I can just get the tools under the more easily. Depending on the size of rocks or gravel, sometimes you have to move them to get to the weeds. I try to avoid spraying chemicals so I have some gravel and some larger rock landscaped areas that are a pain in my rear to deal with weeds.

Stone pebbles are a great way to keep the maintenance down, reduce water consumption, control ground temperature, and more ! however for any trees especially food baring, its important to remember they also need nutrient and that is what earths mulch really is ! Silica dust is one of these useful additives and could be found at most quarries, even for free. There are many great pebbles that can be used, we would suggest the most local pebbles around your space.

Regarding weeds, just put a landscape fabric under the rocks and blow out dirt every so often and this should take care of weeding for years at a time.