"The Elements of Style does not deserve the enormous esteem in which it is held by American college graduates. Its advice ranges from limp platitudes to inconsistent nonsense. Its enormous influence has not improved American students' grasp of English grammar; it has significantly degraded it."
Pullum needs some grammar practice. This (his third) paragraph has five straight "it"s: the first four refer back to "The Elements of Style"; the last, to the entire phrase "American students' grasp of English grammar." By the last phrase ("it has significantly degraded it"), the reader has to wade back through the paragraph for the first "it"; and the last functions more as a "prophrase" than a "pronoun".
"Strunk had very little analytical understanding of syntax, White even less." In this (elliptical) construction, a semi-colon after "Syntax, and a comma after "White" are needed.
After these solecisms, an insightful essay.
Wrong, wrong, wrong.
Second point first: If you put a semicolon after "syntax," you turn the second clause (the one beginning with "White") into a fragment. Semi-colons separate
independent clauses.
First point second: First of all, the issue you point out isn't one of grammar at all, but of usage. Second, there's absolutely nothing unclear about the series of clauses. Third, there's no way to reword it the way you want without violating one of the key concepts of good writing for S&W and a number of other grammarian/usagarians: excise needless words when they contribute nothing to clarity, meaning, or elegance.