Remember that any medic can revive you, but for other classes, only your squadmates can revive. So if I'm assault and not in your squad, I can't revive you.
Some people just flat out have zero situational awareness in this game. I've snuck up on entire squads and melee killed them all one by one and they never notice.
However you don't (or can't) always want to go for the revive. There's lots of situations where reviving one downed teammate just gets more people killed. A lot of people know to wait for someone to revive, and since there's no drag function, you get stuck in the animation for the easy kill. Even using smoke can be tough, as a support player can have a machine gun set up and just shoot until they get hit markers.
Basically, reviving is important, but clear the area first. That animation is so slow and it is hard to get to everyone even if they are seemingly right there. I've been down and basically would rather teammates leave me and give me a place to spawn rather than risk it.