The problem is that T2 effectively ended the story, not only practically but also thematically. The future was no longer determined, we could go our own way, having been duly warned as to the dangers that possibly lay ahead.
T3 never got over this problem and utterly failed to look like anything other than what it was, a shameless cash-in of a popular franchise.
I disagree. In
T2, "Uncle Bob" - a partly-sentient
machine - sacrificed itself to save humanity. But as it and John agreed, the thematic "original sin" - war - started with
humanity ("it's in your nature to destroy yourselves"), and humanity created Skynet. Ergo, thematically, one could well argue that after
T2, there still needed to be a
human atonement for the sins of war.
It makes perfect sense to reason that Cyberdyne's destruction prevented the accelerated,
T1-induced Judgment Day and restored it to its original Air Force/CRS development. IMO - and I admit that this should have been expressed better - the panic that Nick Stahl shows when he realizes that instead of futzing around, he should have been actively working to discover and destroy the CRS Skynet, thus atoning for humanity's wrongs (recall his initials) is what gives
T3 enough heart to justify its existence. Maybe I'm misreading the filmmaker's intentions (the ending narration doesn't quite conform to this), but there you go.
That said, any continuation from
T3 should have addressed his guilt over his failure.