Unfortunately, I think you are alone on this. Sorry. Yes, from a "realism" standpoint, you are right that the shows should be consistent with each other. In theory, yes, we should see the effects of Doomworld on Arrow and Flash. In theory, yes, the spear of destiny should alter the realities of Arrow and Flash too. It might even be interesting to have an episode of Arrow and The Flash that explore how Doomworld has affected them. Those are the only arguments I can come up with in favor it. But there are stronger arguments against it. It would mess up the writing process for Arrow and Flash since those shows have different writing teams. It would confuse the audience who don't watch Legends. And it is not needed since the "doomworld" reality is going to be undone anyway. You are asking Arrow and Flash to move around their stories, insert an alt reality episode that would confuse the audience, only to change everything back once Legends fixes things. It just makes more sense to keep the Legends storyline separate. Plus, from an in-universe standpoint, it could be argued that Arrow and Flash never experience the doomworld reality since the legends undo it. The Legends were directly affected by the new reality so they experienced it but Arrow and Flash only experience the "final" reality after Legends fix things. it is simple and neat.