I'm waiting for any informed answers to your question. All I can give is my
experience, but I don't have a lot to say.
When we started building our school on a dry desert plateau 22 years ago, there was no greenery or other plant matter around bigger than your hand, so we mulched some of the
trees with stones. We were watering our newly planted trees with buckets and later with tiny canals. gradually gradually over the years, some greenery came up along the tiny canals, and there's a bit of shade and microclimate of slight humidity so we don't bother with the stones anymore.
Pros: Stones shade the soil when there's no other mulch available which keeps the moisture in a little longer.
Stones don't get floated or blown away by the
irrigation or wind.
Stones don't hog the irrigation water to themselves like natural mulch would if you were watering from above (but we aren't).
Cons: They don't seem to add much.
Years later I realised that around a lot of trees, the layer of stones was buried under blown in sand or greenery that had come up, so if that's going to be a problem, do think about the fact that it might happen.
I can't say if they actually helped or hindered the pathetic trees planted in the barren desert, though.