Thank you to my teacher and friend Rav Yissie for his thoughtful response.
I think that there is a substantial difference between the effectiveness of tanach study in elementary school as opposed to gemara. It is realistic for a student to graduate eighth grade knowing the story of Chumash, the basic contents of each parsha, most of navi, the megilot, etc. Students can't even learn the basic Pshat of a single masechet of Gemara at that age. I think students memorize better at a younger age, and analyze better at an older age. While a post HS student can analyze tanach well, they can't memorize as well. Most of us will never know melachim as well as bereshit because we learned bereshit earlier. I think Gemara, which requires a higher proportion of analytical thinking to achieve any comprehension, is better suited to older students. Tanach, which benefits from analytical thinking but can be understood at a basic level with a simple read through, benefits from being taught young and revisited when the student matures.
I know this is counterintuitive, but with Torah shebiktav I would aim for outright memorization of the text, because the text is immutable, relatively short, and has cantillation notes that make it easier to remember. The oral Torah, especially the Gemara, is too long for this to be realistic, plus it is more about the concepts than the exact words, the order is far more haphazard, and it has no cantillation marks.
I also think that the values of the Chumash, especially breshit, are comprehensible to small children and serve an important role in their moral development. We cannot possibly wait for students to go to Gush to discover the values of tzedaka umishpat ascribed to Avraham, etc. They must be taught these lessons from infancy. The lessons of the Gemara, aggadic portions excepted, are much more abstract and cannot be digested until a later developmental stage.
I agree that Mishnah does little to develop Gemara reading skills. These must be taught separately, and it is crucial that they be taught in an intentional and structured manner. However, I think mishna does give students the knowledge to understand what context the Gemara is working in. I think that when the Gemara cites a mishna students who are familiar with it already have a distinct advantage because they can better discern the mishna's relevance to the discussion at hand. I also think that it protects students from inventing creative svarot that contradict mishnayot not on the current page of Gemara. Finally there are the many masechtot without Gemara that students should be familiar with as part of basic education. Without that, every Gemara that cites zraim, kodashim, or taharot will seem alien to them.
And to Gary Levine, thank you for your interesting comments, and if you are Rabbi Levine who taught mishna in Yavneh Academy when I was in fifth grade, I thank you for that as well.