Should have been like this:

A team of commandos time travel back and we follow them locating the wreckage of previous fallen terminators while they discuss "saving the future." About 30 minutes in we discover that these guys are going to try to kill John Connor. The death of John created a time split and these humans are from the new arm of time created by it. They have to make sure John is killed or their entire future collapses and they cease to exist. The movie ends up being humans fighting humans with the help of terminator tech. Each group technically "good" as they are simply fighting for their separate futures.
It could even begin with multi-tiered ambushes of time traveling groups preceding each other killing each other on arrival until their ability to do so has been exhausted and the straggler survivors of that melee fade into the plot to arm up for the crucial moment in time (John's death).

Hollywood is run by fools. Millions of dollars flush away in the name of stupid productions. Very few movies are great any more. Always something wrong. Usually something/s very dumb.