Couldn’t we just give it the goal of preventing other AIs from taking over and have it do nothing else?

I could be down for that. The obvious failure mode is that the most efficient way to ensure no other AIs are made is to kill all humans. That reduces the chance of another dominant AI taking over to approximately 0%. I think that closing all the loopholes to keep something like this from happening is just the goal alignment problem all over again, but I could be convinced otherwise.