The Terminator mission would have failed even without Kyle Reese being sent back

Your non sequitur is dismissed.

"With this model, causality is only linear from the point of view of the time traveller."

And in order to write a story that actually works with that model, the events have to work from the perspective of the time traveler(s). In this case, from the perspective of John Connor, Kyle Reese, and everyone else in 2029, the moment the Terminator went through the time machine, he'd been back there for 45 years already, and since they still exist and nothing has changed for them, it inherently means there's nothing for them to worry about. John Connor knowingly sent Kyle Reese to his death, for nothing.

A causal loop story could work in this case if Reese went through the time machine before or at exactly the same time as the Terminator did. It can't work by having Reese go through after the Terminator did, because that instantly adds 45 years of history to the perspective of the time traveler where he can note the fact that nothing changed during those 45 years that the unopposed Terminator had to accomplish its mission, therefore there's nothing to worry about.

Also, I haven't posted a "wall of text" at all in this thread (nor anywhere else, ever, for that matter), let alone "walls of text."

"The first movie, "The Terminator" had a closed loop time travel model."

No.

Some people believe it's a closed loop because of the photo Sarah is clutching at the end.

But she goes on the run and into hiding with the intention of changing the future.

If you believe she changes the future, then it's a case of a different timeline.

If you believe that the future unfolds exactly as it does/did, then it's a causal loop with all its logical and physical complications.

Cameron was going for a Twilight Zone style ending where it's left open to interpretation.

In subsequent movies, he fully tilts into the parallel timelines model.

"That's from the perspective that you can't change time."

The Terminator didn't change time in any meaningful way, which should be obvious to John Connor due to the fact that he still exists and nothing has changed. Whether or not you can change time is irrelevant to my OP.

"However, in science fiction there's the idea that you can change it and it creates some kind of cascading effect that changes history."

Which didn't happen here because John still exists immediately after the Terminator went through the time machine. That means the Terminator wasn't successful in killing his mother. He doesn't need to wait any amount of time to find out the results of the Terminator's mission, because as soon as the Terminator went through the time machine, John immediately has a history where 45 years ago a Terminator tried to kill his mother. And since he still exists and nothing has changed he also has a history where he was born about 44 years and a few months ago, and did all the things in his life which led him to the point of having just witnessed a Terminator go through a time machine, which inherently means the Terminator failed to "retroactively abort" him or otherwise change history in any meaningful way.

You're describing what is generally known as the "Butterfly Effect", essentially the basis of most time travel movies in one form or another. Changes to the past, create a new and different future. The time traveler returns to a new and different present but with all his memories of the original timeline intact.(Back to the Future, various Star Treks, Sliders, The Butterfly Effect, Deja Vu, X-Men, etc).

The other type is the causal loop sort of story where the future creates itself. (Primer, Predestination, the original Planet of the Apes series).

The Terminator is an example of a parallel timelines movie which, superficially, resembles a causal loop movie thanks to that clever ending.

The most clever time travel movie I've ever seen purely from a time travel perspective is Looper. However, even there, the script had to compromise some logic for the sake of a more entertaining story.

Every time travel movie that I know of breaks down if you think about them logically. You just have to accept it in the interests of a good story.

>but when you send reese to a time before the T arrives it would work again.

No, it wouldn't, because if the Terminator was successful, John would cease to exist immediately after the Terminator went through the time machine, and he couldn't send Reese anywhere if he didn't exist. If the Terminator wasn't successful, John would continue to exist and there would be no reason to send Reese through the time machine.

The story can only work if Reese goes through the time machine before the Terminator does, so that he's already a part of the past when the Terminator arrives in the past.

Superficially, this answer sounds good and is probably what Cameron was thinking, as the OP says in his original post.

However, the OP correctly concludes that this answer doesn't make any sense when you give it more thought.

Once the T800 EMERGED in the past, any changes he makes immediately wipe out the future. So, the OP is correct to say the mere fact that John Connor and his team are standing around the portal in 2029 (or whenever it was) after the T800 entered indicates:

i. that the Terminator didn't make it to the past, i.e. was simply disintegrated by the machine;

ii. that the Terminator made it to the past but the changes it made didn't 'stick' and didn't change the future

This is where it gets complicated and where Cameron had to compromise the logic of time travel to make an exciting man-versis-killer cyborg action movie:

There was NO need for John to send Kyle Reese back. If John is alive in the future -- even an instant -- after the T800 went through, it means whatever the T800 did in the past had no effect. No need to send Kyle Reese back.

But Cameron wanted to do a cool action movie with a Twilight Zone ending, so he just ignores the flaw in the logic and hopes we don't notice.

But wait... it gets even more complicated.

It was pointless of Skynet to send back a T800 in the first place. What could it hope to accomplish?

i. If time is a LOOP, then the future is just going to end up where it already is.

ii. If time is a multiverse of parallel timelines, any changes made by killing Sarah Connor in the past are going to create a DIFFERENT timeline with a different future, different Skynet (v2.0), etc.

To the original Skynet (v1.0), it would appear that it sent off a T800 into the past... it disappeared never to return (it's now living in a different timeline much like Marty McFly (V1.0) returns to a different future (V2.0)in BTTF). As far as Skynet (v1.0) sees, nothing changes around it. So why bother in the first place?

"You make a logical mistake that destroys your argument."

False.

"Yes, BECAUSE Kyle was sent back."

No. The very instant that the Terminator went through the time machine, it's already 45 years too late to try to do anything about it. And if you still exist after the Terminator went through the time machine, that obviously means that your mother wasn't killed 45 years ago, before you were born, which inherently means the Terminator failed.