I don't think anything that draws the emotional response T2 did from so many can be accurately described as 'soulless'. If you were to say it was just a remake of T1 and not like it on those grounds, sure. I happen to not care that it's a remake of T1 and in fact admire all the parallels within the two movies together as a duology. I can permit one film-maker aping himself as long as he brings something new. Which brings me to those 'leftovers' from T1 - I'm speaking of the scene where Sarah persuades Kyle that they have to pre-emptively strike back against Skynet. By not including that in T1 it left room to cover it in T2.
edit- and what shows up in my youtube feed today only
Now, a criticism of yours that I definitely can't address is another one of those leftovers - the T-1000. If I'm not mistaken that was another idea Cameron had when doing T1 but the special effects technology didn't exist yet - for which I'm sure you are glad because I know you think the T-1000 delves too far into Marvel superheroes fantasy-land. Fine. I just roll with it because Robert Patrick put on such a good show and I think everything else about T2 remained pretty consistent in quality with T1. And the idea of the unstoppable T-800 reprogrammed and facing an even more advanced Terminator appealed to me as a John Connor-aged child - it was an interesting and new spin at the time - of course to be repeated ad nauseum ever since.