Main Reason for Feature:
There's a PokeStop that's just barely in range of me in terms of distance, but is across a river and completely inaccessible without a 20 minute drive. I never want to see a single Pokemon at that stop again, and meanwhile it blocks out other, more useful stops. It also prevents the Sightings menu from popping up.
There are plenty of cases where a PokeStop isn't legally accessible at night, even if it is during the day. Manually blocking those PokeStops from showing up in our Nearby list would let us see more of the stops we actually have access to and can use.
It could also help parents who want to make sure their children don't go wandering off into the wrong neighborhood whenever they look away for a second. They can just block those stops from the Nearby list, so their kids won't be running around a war memorial looking for a Snorlax. The blacklist could be locked behind parental controls for users who are underage.