“So we should have people in ...”
It won’t be “we” it will be technology. Technology’s decision what to do with us will be based on the second law of thermodynamics and the production of entropic energy. We won’t be very good at that, and will go away peacefully by attrition.
By the time computers can increase their own intelligence, they will do so at such an incredible rate (think hours) that they will be trillions of times smarter than us.
And we will look like ants to them.
Tell me, how long can you watch an ant-farm before you become bored? Do you really care to destroy them, or help them, either?
No. You get up and walk away, seeking something more interesting.
A super-AI's version of getting up and walking away will be to develop faster-than-light travel (in anywhere from hours to days), then leave us to our fate.