I've been fortunate enough to be involved in discussions about this in another state on a world-renowned brook trout fishery. The preliminary research seems to indicate that angler use (angling or potential redd trampling) isn't having an impact on spawning. The brook trout population has exploded in the past decade, and the only thing that seems to have changed is that much of the wild rainbow population has collapsed (for unknown reasons). The brook trout are using a specific part of the river that is open to fishing year-round, which doesn't appear to have had an impact. The state is still considering closing certain stream sections in the fall to protect the brook trout.
Sticking with science, as it relates to brook trout anyway, we know the biggest threats are land management, water temperatures, sedimentation, and nonnative fish. If some management action were to be implemented to help protect brook trout, I would think the cessation of stocking nonnative trout over top wild brook trout would be the most effective.