Understanding and Using Sentence Fragments

Can one be in favor of economy of wording, emphasis, and naturalness of expression and be against the use of sentence fragments?

Fragments use fewer words.
Fragments provide greater emphasis.
Fragments are more natural sounding.

Flesch, Rudolf. (1949). The art of readable writing. New York: Harper.
King, S. (2000). On writing: A memoir of the craft. New York: Scribner.
Schuster, E. H. (2006). A fresh look at sentence fragments. The English Journal, 95(5), 78–83. https://doi.org/10.2307/30046593