They already pushed it with Terminator 3, although it wasn't all bad, the ending was particularly good, as was Arnold's performance throughout. But here's the thing, if there's gonna be no Arnold and it's going to be set during the future war there's just no point in making it other than to earn money.
As demonstrated in the first Terminator, you don't need to show much of the future war, it should just be referenced and you can imagine the conflict. Showing the future war is the equivalent of what George Lucas showed us in the Star Wars prequels. You don't need to see it. Obi-Wan describing it in the original film, describing how Anakin was the best pilot in the galaxy and all that, how the Empire came to be. It's never going to live up to expectations (Revenge of the Sith certainly didn't) so why show it?