I am willing to bet a largeish sum of money that had such a test been around for literacy sometime in 1870 when mass education in the uk started in earnest, we would have found a double hump of people who had a consistent mental model of sentence construction, story arcs, past and future tenses.

The fact almost everyone has same mental model now is down to very early age education. When your parents are literate you will be too.

It's possible this test could be done today in countries with terribly low rates of literacy