I employ all three entrances simultaneously(one is not by choice really). I use the bottom year round, then I prop the supers with door shims above a queen excluder and more often than not, they seem to find a way to use the top as an entrance as well.
The middle is basically a way for them to fly directly to the honey supers to store honey, avoiding the trek up the brood boxes. Just shortens the walk for them. The top, like I mentioned, is not intentional but they seem to find a way in and out of the top, unless I place a heavy cinder block on the outer cover. I'm sure there are plenty of cons for having three entrances, like more bees needed for guards, but it seems to work pretty well and after doing this for two years, I have yet to have an issue with it. I used to use an unlimited brood nest but going through and sorting honey frames from brood frames got old and tiring real fast (I may harvest up to 3 or 4 times per year), hence the queen excluder. In the winter, I put mouse guards on, both to keep mice out and also so the bees have less entrance to guard. I also prop the inner cover with door shims for ventilation.