I think a problem is they tend to get too caught up with the mythology and previously established things to make something great. I mean Kyle Reese is a good example. He's a character we all know and like from T1, I enjoyed seeing his face in the extended version of T2 but then we get to Salvation where I don't even remember anything about him other than him being in it and obviously in Genesys he had to be dug up again because REFERENCE.
For me the best way to go about it in the new one would just be not to include him at all. By not mentioning him or featuring him you at least leave it open that he's out there somewhere, he's just not part of this story. To me this is part of a bigger problem that Redlettermedia brought up with the new Star Wars movies. By constantly putting the same things in your movies you are shrinking the universe. In this case of Terminator, by always having Reese or John Connor or the T800 you're not really proving a point that "we can do anything in this sandbox" but rather you don't really have any ideas for how to expand outside the ideas brought up by Cameron in T1 and T2.
Part of me hopes we do get a good sequel because I like the idea of Arnold as the terminator and Linda Hamilton back and T2 is so amazing that even though I know they can't top it, if they can make a movie at least half as good as it, I will think "hey we had some bad sequels but at least this was a decent entry". I get that the central idea is to prevent John Connor from becoming a leader of the resistance and they tried by killing young Sarah Connor and young John Connor but if you really had the balls you could go back even further to like the late 50s/early 60s and have a terminator sent back to kill Sarah Connor's parents. Plotwise it would perhaps feel like a stretch but the further back you go with a terminator the stronger they become as there's less powerful weapons available to fight them. To reference Redlettermedia a second time in this post they jokingly said in their Genesys review that they should send a terminator back to the wild west and even though that sounds ridiculous, that could be entertaining to watch. At least more than the last 3 movies.