The wording is carefully chosen for these reasons: first, "sheet" has multiple meanings, both denotative and connotative; it is the word used for all kinds of "smooth coverings," such as your bed "sheet," or a "sheet" of ice on your windshield, or a "sheet" of waxed paper over your cooking, or even a cookie "sheet," meaning the flat pan on which you bake your cookies.
Page," on the other hand, strongly suggests paper, either in a book or (in this case) in a notepad or in your printer. A "page" is a "sheet of writing." For an author or essayist or student, the noun phrase "blank page" carries the metaphor of "the beginning 'step' in a long, difficult writing process." Traditionally, the "blank page" is the difficult first step, and its physical appearance is often a psychological impediment to beginning a writing project: "The blank page stared back up at me, and I had trouble writing my first word." A parallel metaphor is "Every journey begins with the first step."