PARKER: "We found this just laying there. No blood. No Dallas."
So what happened to Dallas? Apparently he wasn't killed or eaten; so what did the Alien do to him? The missing cocoon sequence answers this mystery.
More than that, it answers the much larger question of what the Alien's motives are. Up until this scene, it's been nothing more than a nasty monster with a penchant for killing people. Once we see the Brett and Dallas eggs, we get an a-ha moment as we recognise the eggs as identical to the ones from the derelict. Now we understand that the motives of the Alien are one of completing its life cycle.
We also infer that each one of those derelict eggs was originally another victim of the Alien, attacked and parasitised many years ago, perhaps even thousands or even millions of years ago. Once we understand that, we realise that if the Brett and Dallas eggs are left to their own devices they will, in turn, spawn a new source of Alien infestation and the cycle will continue.
Ripley also realises this. That's why she decides to blow up the ship instead of heading directly to the shuttle. She wants to terminate the cycle instead of leaving the eggs to perpetuate the Alien species upon discovery by a hapless space-farer some time in the future. (In the original version of the script she doesn't set the self-destruct until after learning of the egg-morphing.)
In terms of the writing, the cocoon sequence adds a nice structure to the story. The Brett and Dallas eggs create a circularity to the plot in which we end up back at the beginning. We thought we were just watching a sequence of kills, 10 Little Indians-style, but now we understand that the movie has been carefully laying out the life-cycle of the Alien through all its component stages. I find that very satisfying and it's why I think the DC is the superior version.
TC