If he had wanted to, he could have. He didn't want to. Much the same with Terminator 3. He made T2 3D instead.
Personally? I think it would have been great if Ridley and Cameron had done a collab for Alien 3. Jim writing, Ridley directing. I could see that turning out as a solid end to the trilogy, depending on what they did with it.
On the other hand there are a lot of things to like with the Alien 3 we got. Which is why I liken it to being in an abusive relationship. It's not all bad, but the bad hurts me.