I think it violates a conservation law. RSI “foom” to superintelligence is an informatic analog to an infinite energy or perpetual motion machine.
To get smarter you must try to solve real problems in the universe and then do some kind of meta learning (natural selection or some other method of refining the intelligence architecture based on an error signal) to iteratively improve your ability to solve real problems. The error signal is outcome measured against a goal function, which for life is survival (probably reducible to genetic fitness and emergent higher order unit fitness from that).
What’s really happening here is learning. To learn, you must have input. You must have training data.
What is the goal function for RSI? Where does the information come from? How do you know if your recursive modifications are making you smarter or just overfitting you to your own idea of smartness?
I predict the latter. RSI will show transient improvement as the current local maximum is optimized and then spiral off into overfitting.