Maybe in paper, but only on paper. There are so many half baked assumptions in that self-improvement logic.

The moment properly self-improving AI (that doesn't run into some logistic upper bound of performance) is released, the economy breaks.

The AI, having theoretically the capacity to do anything better than everyone else, will not need support (in resources or otherwise) from any other business except perhaps once to kickstart its exponential growth. If it's guarded, every other company becomes instantly worthless on the long term, and if not anyone with a bootstrap-level of compute will be able to also, do anything ever on a long enough time frame.

It's not a race for ROI, it's to have your name go in the book as one of the guys that first obsoleted the relationship between effort, willpower, intelligence, etc. and the ability to bring arbitrary change to the world.

The machine god would still need resources provided by humans on their terms to run; the AI wouldn’t sweat having to run, for instance, 5 years straight of its immortality just to figure out a 10 years plan to eventually run at 5% less power than now, but humans may not be willing to foot the bill for this.

There’s no guarantee that the singularity makes economic sense for humans.

Presuming the kind of runaway superintelligence people usually discuss, the sort with agency, this just turns into a boxing problem.

Are we /confident/ a machine god with `curl` can't gain its own resilient foothold on the world?

Your logic might make intuitive sense, but I don't think it is as ironclad as you portray it.

The fact is, there is no law of physics that prevents the existence of a system that can decrease its internal entropy (complexity) on its own, provided you constantly supply it with energy (negative entropy). Evolutionary algorithm (or "life") is an example of such a system. It is conceivable that there is a point when a LLM is smart enough to be useful for improving its own training data, which then can be used to train a slightly smarter version, which can be used to improve the data even more etc... Every time you inference to edit the training data and train, you are supplying a large amount of energy into the system (both inferencing and training consumes a lot of energy). This is where the decrease in entropy (increase in internal model complexity and intelligence) can come from.