"Select a cold-water stocked stream that is considered a nursery stream
Do a baseline survey noting young of the year and age class structure on the selected stocked stream
Stop further stocking"
These nursery streams are wild trout streams.
And many of us have been saying for years that stocking should be ended in wild trout streams. Fisheries biologists have been recommending that since the 1940s. Trout Unlimited was formed in the mid-1950s for the purpose of advocating ending stocking over wild trout.
So, yes, stocking should be ended in wild trout streams, whether or not they are considered "nursery" streams or not.
Just about any wild trout stream could be considered a "nursery" stream, i.e. trout can move back and forth between smaller and larger waters, unless there is some kind of barrier to passage.
Do the right things and you'll get good results. End stocking over wild trout. Remove barriers to passage. Improve riparian and floodplain vegetation. Reconnect streams and their floodplains. Restore streams that have been straightened, channelized, diked and bermed, etc.
If the habitat conditions of the streams with year around populations are improved and stocking is ended on them, their populations will go up. That will improve the numbers of runners as well as the number of stayers.