... I think for all the missteps of T3 though, it was Salvation that truly sank the franchise. Then Genisys buried it. ...
Though it was mostly a rehash of T2, T3 was at least enjoyable in my opinion. Salvation was a very poorly executed step/stumble in the right direction... and yes, I agree, Genisys was cr#p.
I think the Terminator franchise needed to reinvent itself similar to how the Fast and Furious franchise did. Let's be honest, the first F&F movie was basically Point Break with cars instead of surfboards. 2 Fast, 2 Furious and F&F: Tokyo Drift was more of the same (modified cars, hot girls, street races, etc...). Then over the course of F&F4, 5, 6 and 7, they recreated the franchise from a bunch of regular young adults with fast cars to movies where the characters became essentially a tier 1 special operations unit (or James Bond, or a Marvel superhero group... take your pick) and the action sequences were crazy and fun, though not necessarily believable. The characters were visibly older and changed and the movies reflected that. I know some fans of the original didn't appreciate the change, but movie going audiences in general seemed to.
Back to Terminator though; I think the time travel thing should have been abandoned. Obviously it was an integral part of T1 and worked well for T2 and well enough for T3, but that's where it should have stopped. Salvation was the correct place to start for T4, though it should have been darker. The human resistance should have been a few scattered groups, barely surviving and not an organized military like we got with the movie. The audience could have followed John Connor as he slowly built the resistance into a trained fighting force with maybe the end of the movie being some sort of win for the resistance and John, cementing him as the legendary hero. T5 would have been an ESB/Avengers:IW type movie with the good guys losing at the end, then T6 would have had the resistance destroying Skynet only at the end, observing the T800 and T1000 being sent back in time, thus repeating the cycle.