Alien was never supposed to be a movie about serial killers or science gone wrong. It was supposed to be about something that confronts every fear we have about ourselves and our beliefs. It's supposed to confront that part of men that believe women are just home maker vessels for children and turns that belief on its head by shoving the very disturbing belief right in front of them. They are now the vessel, they are now the home maker. And they have no organs to carry out that ability, they have no way to escape the desires of this thing towards them whose side effect is unbelievable pain.
The Alien is the industrial man getting his way with someone who just wants to create more of himself. It isn't supposed to be scientific, it just is about entering the disturbing notions that industrial society needs to run on. Pain and sex. Something men often don't think about fully, but it's shoved into our face with Kane first being raped, then giving a fatal birth.
This is right up HR Giger's ally and why he probably nailed a skull into it under the dome. The skull is required because its a bit of a garnish on the whole thing. You think you see a skull, but you're not sure. The alien is uncaring lust and uncaring death, and tries to hide its true face, the face of a skull, the face of demise.
However you were never really supposed to see the skull up close in certain lighting conditions, just brief glimpses of what appears to be a skull. So showing too much of it misses the point, but showing none of it all also misses the point. It's a subtle addition to the creature that says basically its intentions may seem only animalistic, but it is truly "human" in a way men usually do not comprehend fully
The beast isn't supposed to just look "cool", HR Giger made the decisions he made making the costume to try and explain what it represented. Removing the skull removes a part of the design, it is supposed to be there, but it shouldn't be fully visible. It should just show the illusion of a human face under the dome to tell the audience that this thing is much more human than you want to admit. Which given the topic of this thread, is kind of funny