I think it's because they ran out of bullets, and they self destruct. Also, I have been observing this for quite some time now. I think killstreaks have time limit or duration. I hope this makes any sense.
Like what gramthenOOb said, it would be to provide a fair gameplay. I mean, think of it this way. If the enemy team got first dibs on turrets and they won't destroy overtime, would it be a fair gameplay? It has something to do with balancing gameplay.