Militaries depend on poverty for labor. Recruiters don't prowl around private schools in rich neighbourhoods. They focus on poor neighbourhoods. The problem is that once general AI is achieved, and the majority of the human population become unemployable, it's gonna be hard to have people just straight mass murder the masses and cull the human population down to what is sustainable long term... That's where the AI killbots come in!
The future in Terminator is set in the year 2029. The movies just missed the mark by a few decades so we can expect the machine uprising in 2029 and the future hellscape ruled by machines is 2049.
That's the entire premise behind the US and Israel hacking Iran's nuclear plants (remember Stuxnet?), they don't want Jihadists to get access to devastating weapons because they will use them against the US too, any chance they get.