I kinda feel like just a few small changes in the script could have made it better or at least avoid those "we've seen this before moments". Just throwing out a few ideas now. SPOILERS
1. How bout instead of the distress beacon which makes them change planets, how bout go for something different? Maybe they arrive close to their original planet but it turns out they did their calculations wrong or something has changed (like a giant meteor has crashed with that planet) or just something that forces the crew to pick an alternative planet rather than deciding to do so because of a signal. Because the travel time to the planet is a very long trip spanning years, so something could definitely have changed in that time.
2. When we finally get to the egg/facehugger moment it's all happening because the captain is following David's advice and sticking his head down an egg basically. How bout changing it so that when the captain killed the Neomorph (which upset David), David could have knocked him out unconscious and dragged him down the cellar. Could have been a tense scene of the captain waking up in the egg room and them beginning to open, which would have made us (and him) go "shit get out of there" rather than "why the fuck are you going close to the eggs?!". Instead of mimicking the John Hurt moment of the first Alien, we could have had the captain actually being smart and trying to escape the room with multiple facehuggers attacking him, finally he can't fence them off and one gets on his face. That way his fate would have been less idiotic.
3. Not showing the Alien birth on the ship at the end was a missed opportunity because those moments are for the most part really well executed. Having Daniels wake up to the "there's an unknown lifeform on the ship" wasn't as great as if we would have seen it. I feel like most people (myself included) were slightly surprised because the guy only had a facehugger near his face for 15 seconds or so, could have made something interesting of that birth scene on the ship.
4. A few more flashbacks could have helped to really bridge Prometheus and Covenant and especially David's motivation. Sure, we get that he is basically Doctor Moreau and wants to breed Xenomorphs, but I would have been really curious to see more scenes of him and Shaw. I don't think there's any way that she was 100% supportive of his decision to go full holocaust on the engineers but on the other hand her corpse looked pretty fresh when they found it in Covenant. Not "she died 10 years ago" but more recent. Would have been interesting to see the moment of betrayal when David decided that he needed Shaw to give her life to reach the next step in the Xenomorph evolution chain. Because after she put him together, that could have been a powerful scene.
Just throwing out some ideas, what do you guys think?