In Terminator 3, the T-800 tosses out a damaged fusion fuel cell that explodes in the desert. It has two of these things in it. Every Terminator has these fuel cells. Ergo, every Terminator not only carries a nuke, it could carry many more. Does a Terminator need that right arm? Implant an arm-sized nuke under that living tissue, and all it needs to do once it goes back in time is rip its own arm off and then blow up L.A. Make its entire chest cavity a nuke. Or give it detailed files on how to mass-produce fusion reactors and have it explode everything everywhere. Get festive with it, man!
Your second issue here is nicely wrapped up in Terminator 2 itself; you don't even need to hit a new installment to tear that flesh argument down. The T-1000 is a mimetic poly alloy. Which is to say it imitates flesh, but it is not made from living tissue, like a Kardashian. So why the hell isn't that goo on everything? They put it on the T-X in Part 3 so it can smuggle guns.
Why not put that stuff on those giant HK robots that run around in the future? Who cares if it can't blend in with humans? It's like a robot crab the size of the Hulk armed with machine guns. What the hell in 1984 is going to stop it before it tracks down Sarah Connor and vaporizes her?
Why not literally put poly alloy on a nuke the size of a bus and just send that back in time with a 10-minute detonator on it and blow the whole county off the map? Why must all Terminators look like people? Who is Skynet trying to fool at this point anyway? It never works, so why bother?
Oh, fuck you, Salvation. You weren't even trying.
Of course, we've covered all this before, but there's still one other option Skynet hasn't considered: Skynet itself is a program. In Genysoceros it actually has an avatar, a body that the living program resides in. Why the hell didn't Skynet send itself back in time as a Terminator? Ever? It would literally make the entire franchise obsolete in one single time-jump, and all the efforts to stop it would be for nothing. No one could prevent Judgment Day, because it is literally the embodiment of Judgment Day. All it would need to do is access a network, which it could do wirelessly the minute it arrives, upload itself, infect every computer everywhere, presumably in no time flat since it's fully sentient and futuristically advanced, and launch all the missiles right then, before anyone could hope to prepare. Done. End of series.
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