Elsewhere in the thread, it's brought up that AI could move faster than corporations generally move. That might be true, but there are still physical limits: the speed of light, moving mountains of steel takes energy, etc.
What do you mean by this?
At some point it had more soldiers and controlled a greater subject population than the government of Britain itself.
I'm not sure it was ever profitable, though, which is the main paperclip corporations ostensibly maximize. Which itself speaks to the problem: superficial objective functions don't always determine outcomes or behavior.
Individual corporations aren't capable of unbounded exponential growth because they can't keep the interests of the humans that make them up aligned with the "interests" of the corporation indefinitely. They develop cancer of the middle management and either die or settle into a comfortable steady-state monopoly.
Market systems as a whole can and do grow exponentially - and this makes them extremely dangerous. But they're not intelligent and so can't effectively resist when a world power decides to shorten the leash, as occasionally happens.
That's key to the story of the paperclip maximizer - the paperclip maximizer will go about its task by trying to improve itself to be able to best solve the problem, and once it's improved enough it will decide that paperclips would be maximized by destroying humanity and would come up with a plan to achieve this outcome. However, humans may not realize that the AI is planning this until it's too late.
A human+ level AI would be able to understand and improve its own hardware and software in a way we can't with our own brains. As it improves itself, it will get compounding benefits from its own improvements.
Corporations are not capable of having the "fast takeoff" which is an integral part of the doomer narrative here. Furthermore, a corporation being a paperclip maximizer is an abstraction that obviously falls apart in the extremes, if for no other reason than because at some point destroying the world for the sake of more paperclips is going to have a negative ROI....
Meanwhile, the (AI) paperclip maximizer is actually trying to maximize paperclips and does not have the sort of internal checks that would apply to real-world orgs. That is the crux of the problem.