Maybe World War III was not the fated event of the Beta timeline since the time travel documents were destroyed in the plane crash. That doesn't kill the possibility that another conflict may arise however.
If John Titor doesn't show up in 2000 or 2010, chances are they're not in the Beta world line anymore. You can check that with a simple Goodle search.
I guess that they are still stuck but not in the Beta timeline but in the Alpha timeline where the badges show up.
The badges in the final Worldline are different from the one Suzuha has in the Alpha Worldline
The event that led to all the series happening was the D-Mail Okabe sent to Daru telling him about Kurisu's murder. He can't undo this without causing a very serious paradox. But he can change the events that made him believe she was dead and send that mail, and he can also change the side-event that led to WWIII- the doctor carrying the paper on time travel to Russia, which is in no way strictly tied to him witnessing Kurisu's death, the key event of the 1% timeline. The same way he could create different versions of the 0% timeline, where Rumiho would have an alive dad or where she wouldn't, but in which Mayuri would always die, here he can create several variations of the timeline where he sees Kurisu "dead"- one where there is a WWIII and one where there isn't.
For the record, in the game at least, Daru mentions that the specifics of Kurisu having died were actually fully covered on the news-ergo, Okabe does in fact change history by traveling back in time.
One thought. I'm currently watching Chaos;Head and here's the thing: The whole universe is created from PERCEPTION. In Chaos;Head the bad guys convert images shown to people into reality, maybe the timeline works the same way? So it really doesn't matter if Kurisu dies, what matters is that Okabe sees her in a pool of blood. If he tried to pull it off the same way with Mayushii, it would probably work
Ever wonder why Okabe's ability is called "Reading Steiner"? His ability to preserve his memories and from his method of timetravel is the same as the viewpoint of the audience. Now what was Steins;gate adapted from? A visual novel! That means that Okabe's power is to share the viewpoint of a reader, essentially 'Reading Steins;gate'
Notice how in the manga/anime Amane Suzuha has such a weird salutation: (O-haa!)? The reason why she doesn't know the current trends in saying hello is because she's from the future.
Also worth noting: that salutation was current around 2000, when it almost immediately fell into disuse.
Fridge Logic: How does a little girl manage to push a fully grown woman far enough to get hit by the subway? Granted Mayuri is small and was caught off guard, but it still defies physics. It's even worse in how Nae pushed Mayuri by tripping.
Diabolus ex Machina at work perhaps? She was fated to die anyway. I think Nae tripped and as Mayuri saved her, she fell off as a result.
If you revisit the scene, she trips and then nudges Mayuri into the track. It wasn't a situation where she would've fallen into the tracks and Mayuri sacrificed herself.
When they successfully hack into SERN and find all of the reports of the dead human subjects, why didn't they just go to the police and have that organization arrested for unethical experimentation? Sure they might have gotten that information through illegal means, but it should still have been considered at the least.
Okabe was blackmailed.
Yeah, but that was for quite a while after they found those reports.
SERN has the ability to cover up events. Including murder in Gamma timeline.
Fridge Brilliance: Connections of Episode 1 and 24. It was the same voice Okabe as he tried to fake the death of Makise Kurisu on episode 1.
Future Okabe actually ensured Operation Skuld's success.After the first failure, Future Okabe's worldline exists in a concrete enough form for the movie mail to go through. If Future Okabe's assist fails to produce a successful outcome, Okabe will simply become Future Okabe, at which point he sends the movie mail again (possibly with changes to the script) and the cycle repeats until Okabe actually succeeds. "The world is in the palm of my hand," indeed.
Looking at the kanji used to write "Stein's Gate" in the visual novel makes the implicit explicit by rendering the term as, loosely, "Stone Gate of Fate." Okabe is told that that name was given to the target worldline specifically for the reason that "it doesn't really mean anything." Future Okabe tells him this as he charges him with his final mission to change the future. In other words, Okabe is being reminded that there is no fate but what he makes.
Alternatively, Future Okabe is naming the new worldline Stein's Gate purely because it does not actually mean anything (yet). Okabe often refers to meaningful events as "the choice of Stein's Gate". If Okabe succeeds in moving to the new world line, those statements will no longer be meaningless, as the phrase "choice of Stein's Gate" will become synonymous with the phrase "choice of the current world line".