That would have worked if it was set on the same planet as Alien (it's not), but then you'd have the implausibility of fossilization occuring in a few decades instead of hundreds of years. Of course, the premise of Prometheus is implausible in the first place so maybe people would let that slide, it's hard to pin down these sorts of technicalities when some are accepted and some seem hard to swallow, personally I feel that would violate the movie's logic somehow, although I probably would not be complaining too loudly if they did go that way.
What interests me more is the fact that the engineer in Alien is of different design and proportions than in Prometheus. It's at least 25% larger, and it's not an astronaut sitting in the chair, the astronaut is the chair. I think this is one of the most overlooked aspects of Giger's design in that he seems to be implying that the being is part of the ship, that the ship itself is alive, which explains all the bone shapes and organic parts to it, and the beings and the ship are basically one and grow into each other using some sort of technology we can't even really grasp. I guess this is similar to the BSG ships that appear to be craft but are actually organic beings. Because even though Dallas says it looks like it has grown on to the chair, it hasn't, the chair design actually overlaps into his body as one cohesive design. In fact, if you look at the proportions, it doesn't even look like his legs could "fit" in the chair, it's like this weird being growing out of some sort of pod on the ship.
I'm sure though that they were originally prepared to ignore that, and the original script certainly seems to have.
I've noticed though that in the scene where David finds the pod cargo hold near the end, the gate he passes through has two enormous guardian statues that hold an uncanny resemblance to that original Alien astronaut, as long as you accept that it wasn't part of the ship itself but a being sitting in the chair. They shrunk down the engineer for Prometheus, changed his design and changed the design of the chair as well as his space suit. But then there are those giant statues that look a bit different. Maybe there are more than one type of Engineer? Would that be related to the giant head in the pod room? It has religious overtones, and the "engineer" artifact in Alien realistically would have been thousands of years old. Lots of interesting questions raised. I think Prometheus 2 may have some additional clues....or maybe they just accepted a few design inconsistencies. Personally I think either possibility is equally likely to be true.