As you say, the key issue is goal stability. OT is obviously sound for an instant, but goal stability is not clear.

What is clear is that if there are multiple AIs in any sense then and if there is any lack of goal stability then the AIs that have the goals that are best for existence will be the AIs that exist. That much is a tautology.

Now what those goals are is unclear. Killing people and taking their money is not an effective goal to raise grandchildren in human societies, people that do that end up in jail. Being friendly to other AIs might be a fine sub goal.

I am also assuming self improvement, so that people will no longer be controlling the AI.

The other question is how many AIs would there be? Does it make sense to say that there would only be one AI, made up of numerous components, distributed over multiple computers? I would say probably not. Even if there is only one AI it will internally have a competition for ideas like we have. The ideas that are better at existing will exist.

It is very hard to get away from Natural Selection in the longer term.