I'm going to largely duck your last question: I doubt even the most enthusiastic proponents of the death penalty believe it should be imposed for every murder. Most jurisdictions distinguish between first-degree murder, second-degree, etc., precisely because not all murders are morally serious enough to merit the death penalty (which it is not to say that any murder merits the death penalty).
But on to your main question: Should the death penalty be automatic for murdering a law enforcement officer but not automatic for murdering anyone else? I can think of three possible rationales for an affirmative answer. I'm not sure I find any of them convincing, but I'll leave that to your judgment.
The first is that killing law enforcement is morally worse than killing someone else and so automatically deserves a harsh punishment. Your position seems to be that this is not so: That in order for killing law enforcement to be morally worse than killing someone else, there must be something about the officer that lends the officer more 'intrinsic worth' than the typical citizen. I agree that is probably not a very promising way of explaining how killing law enforcement might be morally worse than killing others. But a slightly more attractive thought is that killing law enforcement reflects more negatively on the character of the murderer than does killing someone else. Perhaps killing law enforcement shows greater contempt for law and legal norms.
A second possible way to defend the automatic death penalty in such cases is to suggest that because police work is inherently dangerous, the law should impose additional penalties on killing law enforcement in order to discourage such killings. Law enforcement are unusually vulnerable to be killed, so preventing them from being killed may require punishments that are harsh and unambiguous. A further consideration of this sort is that perhaps it would be harder to recruit police without this harsh penalty for killing them.
A final rationale rests on what's often called the 'expressive' theory of punishment. This view says that punishment is justified as our moral condemnation of a criminal's wrongful act. If the killing of police induces greater outrage than the killing of others, then (according to this theory), those who kill police should be shown less leniency than those who kill others. Obvious question to ask here: What, if anything, justifies our greater outrage at killing law enforcement? It might seem that this rationale ends up requiring, or collapsing into, the first: that those who kill police show themselves to be morally worse than those who kill others.
And let me add: Great question! (To my knowledge, philosophers haven't taken up this issue directly.)