If AI is limited by hardware rather than insight, I find it unlikely that a 300 trillion parameter Transformer trained to reproduce math/CS papers would be able to "go foom." In other words, while I agree that the system I have described would likely be able to do human-level programming (though it would still make mistakes, just like human programmers!) I doubt that this would necessarily cause it to enter a quick transition to superintelligence of any sort.
I suspect the system that I have described above would be well suited for automating some types of jobs, but would not necessarily alter the structure of the economy by a radical degree.