Is it ever ok to take a pebble from a stream as a souvenir? (Asking for a friend)
It depends on the jurisdiction. In National Parks, it is literally, take nothing but pictures, leave nothing but footprints (and in some locations, even those are verboten). In National Forests, the rules are somewhat less restrictive, but technically, for most collecting, you ought to have some sort of a permit. Most state park systems have curbs on collecting.
Of course, there are jillions of pebbles in every stream bed, and you can well ask, what difference does one less make? Actually if there is high visitation, intermittent, occasional collection can make a huge difference.
I once excavated a major Pueblo ruin in canyon de Chelly NM which when we first started, showed absolutely no potsherds (broken pottery fragments) on the surface. By the end of our digging, we had collected thousands of fragments and they were important in our analysis. I got so I could assess the frequency of visits at any site by the abundance of pot sherds showing on the surface. Visitors mad made a considerable impact on the information available from the sites within the canyon.
Yes, pebbles are pretty ubiquitous and if you are in a truly remote area with minor visitation, picking up a pebble probably won't make a difference. But just taking a picture is a safer bet.
Just send me the ones that are clear and that scratch window glass readily. I will take good care of them for you.
Can you tell that I am an old NPS hand?
leave no trace is exactly that. Try no to impact the environment so the next person can enjoy it as well. Since millions hike the trail, if everyone took one, you just redirected the river...
Ah, but you are leaving a trace! You are compacting the soil (and maybe crushing plants). By the time millions will have followed, the rivr will be redirected.
This is actually observable, on a slightly different scale, in some locations in the Arizona dessert, where vehicle tracks are now streambeds.....LNT is highly admirable, but hard to do.