Because it clearly does.

Let me be clearer:
* Turn 1: The city is dimmed. I can't see the units in the city, and I can neither bomb nor unit strike it. I can, though press R for a recon mission. The plane flies over, and, voila! Now I can see the units. Now other planes from that same city can bomb and/or unit strike, for exactly the reasons you list.
* Turn 2: The city is clear, I can see what's there, I can bomb and/or unit strike away.
* Turn 3: The city is dimmed again. I can't even see the units in the city. In order to see them again, I have to spend another recon mission.
Note, this is NOT the situation you describe--where I can see the city, but the strike graphic never turns green, either because it has no defenses left, or there are no units left to strike.