That's the logic I was avoiding, because although it's heuristically likely in real life that there's only one culprit – and that you could get Bowl 9 with ingredients a, b, c, d, e, f, and g to show it's definitely h or i if you don't get sick – there's also a chance you have diarrhea on that Bowl 9 and gain very little information. There's no conclusiveness to the variable isolation, so it's not sound from an information theoretic perspective.

Actually, if you assume a comically unlikely worst-case scenario where all of the ingredients cause diarrhea, that sort of recursive algorithm might be the most amount of diarrhea you can get while still gaining information on each bowl.