Correct me if i'm wrong but I wanna say there was some explanation that Skynet couldn't just send back a Terminator to whenever in time because the time travel would only go back as many years - though this explanation is something i'm not sure if i heard from one of the movies or if i dreamt it up, it could all just be in my head.
From just a movie perspective the idea of sending back a Terminator even further to kill X Connor to prevent the future birth of Sarah/John could make for some different flavor and you could have a movie set during WW1 or WW2 or even go back further like during the wild west or something. There are creative elements there and you could have fun with certain elements. The two good upsides I can think of other than the movie having a completely different setting would be 1. the terminator would be more menacing because there's less powerful weapons back then so fighting it would be a lot harder, 2. even if you send a protector back, you could still get some freshness with a Connor as a main character who isn't already clued into what's going on. The downside for me would be that we're basically re-telling the same story just changing the packaging.
It could have been interesting if John Connor grew up to be just a normal guy because of the pressure of knowing who he would become and the trauma from T2. (Though this might contradict the rules of the time travel which is sort of a loop i guess) I still enjoyed Dark Fate but I feel like at this point just let this franchise rest for 5-10 years and then try a back-to-basics reboot without any of the actors from the other movies. A low-budget Terminator made by Adam Wingard who made The Guest or Leigh Whannell who made Upgrade or something like that. Keep it a bit more grounded, more practical effects less CGI explosions. Maybe bring back the T-800 as the villain and just a human sent back as the protector. No more crazy new Terminator robots.