As I understand it, Eliezer Yudkowski doesn't do much coding, but mostly purely theoretical stuff. I think most of Superintelligence could have been written on a typewriter based on printed research. I also suspect that there are plenty of academic papers which could be written by hand.

However, as you point out, there are also clearly some cases where it would take much, much longer to do the same work by hand. I'd disagree that it would take infinite time, and that it can't be done by hand, but that's just me being pedantic and doesn't get to the substance of the thing.

The questions that would be interesting to answer would be how much work falls into the first category and how much falls into the second. We might think of this as a continuum, ranging from 0 productivity gain from computers, to trillions of times more efficient. What sub-fields would and wouldn't be possible without today's computers? What types of AI research is enabled simply by faster computers, and which types are enabled by using existing AI?

Maybe I can type at 50 words a minute, but I sure as hell can't code at 50 WPM. Including debugging time, I can write a line of code every couple minutes, if I'm lucky. Looking back on the past 2 things I wrote, one was ~50 lines of code and took me at least an hour or two if I recall, and the other was ~200 lines and took probably a day or two of solid work. I'm just starting to learn a new language, so I'm slower than in more familiar languages, but the point stands. This hints that, for me at least, the computer isn't the limiting factor. It might take a little longer if I was using punch cards, and at worst maybe twice as long if I was drafting everything by hand, but the computer isn't a huge productivity booster.

Maybe there's an AI researcher out there who spends most of his or her day trying different machine learning algorithms to try and improve them. Even if not, It'd still take forever to crunch that type of algorithm by hand. It'd be a safe bet that anyone who spends a lot of time waiting for code to compile, or who rents time on a supercomputer, is doing work where the computer is the limiting factor. It seems valuable to know which areas might grow exponentially alongside Moore's law, and which might grow based on AI improvements, as OP pointed out.

You'd be amazed what people can do "by hand". Keep in mind, computer was originally an occupation.