Chekov's Gun can rarely, if ever, improve a story. While a lot of people seem to fall for Chekov's Gun, I don't think that those who are aware of it usually consider it to be a mark of a good story. At worst, it's obvious that the writer is bullshitting its audience. Chekov's Gun is just one of the many reasons why Abrams/Kurtzman Star Trek is basically on fire right now.
> - Multiple-universes time travel. Why stick with an existing world and its background when you can just replace it!
I don't think people are bothered by time travel plots because of the infinite possibilities to change the setting. They dislike time travel because it's usually too easy to travel through time, and shows or movies rarely adhere to any consistent time travel mechanics. Time travel stories are good at conveying high stakes, but they almost always lack any real consequences. When someone brings up time travel as a solution, nobody ever says "You know, the last time we traveled through time, we all nearly got killed and almost destroyed the universe."