Atlas would have actually only been PRETENDING to be Frank Fontaine, as the real Frank Fontaine did die, but Atlas set all this up and had you kill hundreds of people BECAUSE IT'S THE ONLY WAY
You would have had lengthy two-way conversations with Atlas over the radio, and had a boss fight against Ryan where he ran around the room before you drained his health bar. Once the fight was over, a blood stain would suddenly appear on his shirt with no obvious wound, and he would lie down and explain how he's your father and how you were trained and all that, and then would quietly die in your arms. Lighting effects would give the appearance of his ghost escaping his body while Jack shook his head and cried.
But again, he's not really dead.