They've been toying with the "John isn't required to save mankind" idea for a while. T:TSCC played the most with that idea by really hammering down the time travel mechanics (ie, multi-verse).
It is sort of like the "what if Hitler was killed as a child?" thought exercise. The "kill Hitler" thing toys with the idea that if Hitler was killed off as a kid, then WW2 and the holocaust would have never have happened. But that is a gross simplification of things. WW1 still happened and Germans were still pissed at the punishment levied upon them. Strong anti-antisemitism still existed. Someone else could have easily taken the same role in the Nazi party and taken Hitler's place. Hell, without Hitler, maybe Germany would have even won Europe (since Hitler was an egotist who ignored a lot of military advice from people who knew better, resulting in opening up the Eastern front much earlier than he should have and hamstringing German military response during D-Day). I don't really have a problem with them killing off John or even changing Skynet. I kind of like the idea of a changing multiverse brought about by changes they do, and how no matter what they do, the future will always eventually find a way to make specific things happen anyways because the underlying things that cause those future events still exist.
You're absolutely right. But you've also inadvertently hit on why these movies don't feel very satisfying. Because their themes are all fucked up and often downright contradictory. For example, as you described--the basic gist of what you described is...Fate. Things are fated to happen because forces that bring them about are larger than humans can control or any single human can change. Fate. Except the ENTIRE point of the Terminator one and two is that you have the power to...change your fate. And its clear they still attempt to adhere to this theme too, despite their entire film now showing how its wrong. Check out their movie posters if you don't believe me.
When Jen Connor becomes the fully realized "head" of the human resistance (When the hybrid tells her) there is a flash back scene where she says "Fuck fate". That's the entire point of her character is to
fight against fate. But we've just watched how that struggle is useless. John Connor was supposed to fight against fate too, and he
won that struggle...and what happened to him? He wound up dead and the same fate happened anyway with a new Jen Connor. There is no denying fate. If you won't cooperate, you'll simply die and fate will continue with someone else who is exactly like you.
The movie's entire theme is that the struggle to survive is pointless. Your actions are pointless. Even if Skynet 2.0 manages to kill Jen Connor,
her very existence illustrates she is ALSO inevitable, and that said AI is also destined to lose the war. Meanwhile, every element within the movie is still trying to obtusely say "our fate is ours to choose"...What? No its not.
Clearly its not. Unless you mean the choice to die or accept it, but you'll never live in a world that's been fundamentally changed by you in terms of how its supposed to be. Its inadvertent, depressing nihilism, and what's worse it makes the characters seem hollow and silly. Because they earnestly pursue the notion they can 'fuck fate', while stubbornly ignoring all the evidence they can't, without even a moment of self reflection on that fact--either they are idiots or vehicles to advance the plot and neither make for characters that are easy to sympathize with.
(And this is the issue with time travel movies in general, its why you can't really make sequels of them. Either your sequel illustrates you're stuck in a time loop that will play out in different ways to the same conclusion FOREVER, IE what Terminator is doing, and that's boring (Or horrific, and the only way you can make a good film is to acknowledge and confront the nihilism of it and make a story about that). Or you do what happened in T2 and show time travel is a true wildcard that disrupts fate/determinism and make your story hopeful.)