That has not been my experience as far as light though I would agree that they don't like or need very strong light, they are photosynthetic. I have more than a dozen now and all are on the bottom of the tank but not in the shade and I have some serious lighting on my tank. Granted the tank is 24" deep.
OP, if it does die, don't remove it. I had one Fungia die in my tank and it's constantly shitting out new plates. I have at least a dozen from it and even a year later, it's still producing new fungia. Also, I don't think it's your alk. Natural sea water is around 7.5 dkh. 8 in my opinion is just fine. Some corals can be finicky but one thing you didn't mention was the age of the tank. They really do best in a mature system and as such, i wouldn't recommend them for a tank that is under 12 months old. You also didn't mention your livestock or if you did, I must have missed it. Some fish may pick at them which will irritate them. As for bristle worms, as noted above, their populations are typically limited by the amount of waste and detritus in your tank. Judging by some of the macro growing on your rocks, the presence of some cyano that I see and the amount of worms you have in your system, that tells me you need to work on your husbandry. Vacuuming, blowing the rocks off, staying on top of Po4 etc. Lastly, bristle worms are detritivores/scavengers. They don't usually mess with corals.