The defenders from C on Rooftop can push to the lanes and make your cover fire from the bridge completely useless however. Defending a lane as a sniper is generally a lot better. The problem with objective C on Rooftops is that no one on the attacking side can see around the big generators/air conditioners in the middle of the objective. The entire enemy team can be back there canceling out a capture and there's not much your team can do. The best way to clear out behind that objective I find is to try and coordinate a rush of abilities. A Blitz and HEAT or an AEGIS are a great way to get your team around to the back and clear out the enemy. However once you've done that you can't really keep them away from the objective without being called a spawn killer/trapper.
What did the snipers on the bride do during this? Absolutely nothing since they have such a limited FOV behind the objective. Had they been down in a lane they could have pushed up and helped clear the backside of the objective, or even sniped people dropping down from the defender spawn (at risk of being called a spawn killer/camper).
And that's basically why I don't like sniping from the bridge. Limited view to the important areas.
I love snipers on the bridge. I run right up there and punch them off with my armored elbow.
When you are at or behind the cap and you are defending, that space in front of the cap is open territory for the opponents to move up. Push up, close the open territory. Then your flanks are also less open.