String length tells you the frequency with which nul terminators will be found. Without knowing frequency of occurrence of the nul terminator, 's', and 'p' then you cannot know which one occurs most often.

Consider two benchmark cases: (1) every string tested contains exactly one character (2) every string tested is 1MB long and is composed entirely of 's' and 'p'.

The author's first "optimization" assumes nul is rare. It would make benchmark (1) worse, and (2) better.

The article is a good example of "specification is hard, code is easy." He insufficiently specified the problem to be solved, and his test cases contained information not in the code and not in the text of the article.

We know that E[# of '\0' in a string] == 1.

But what is E[# of 's' in a string]? Is it greater or less than E[# of '\0' in a string], and how should the compiler know this?

You haven't given the compiler any reason to assume that 's' or 'p' will appear more often than '\0'.