Are “unlevel / unleveler” not so common words?

Question

Suzanne Mettler, a professor of government at Cornell University wrote the article under the title, “College, the Great Unleveler” in New York Times (March 1). She pointed out that the degrees of inequality between the richer students and poorer students in higher education in U.S. is widening by saying;.

"Most of us were raised to believe that going to college was the surest path to a better life, but for many today that belief can be perilous. Unless we can claw back polarization and plutocracy enough to restore opportunity in higher education, the United States will become a society in which rank is fixed and our ideal of upward mobility but a memory."

http://opinionator.blogs.nytimes.com/2014/03/01/college-the-great-unleveler/?_php=true&_type=blogs&hp&rref=opinion&_r=0

Apart from her criticism on polarization of opportunity in higher education, I was drawn to the word, “unleveler,” which I thought a pretty common word, because of its shortness and easiness to understand due to the simple construction of “un＋level.”

However, when I checked the word on online Oxford, Cambridge, Merriam-Webster English Dictionary and Collins Cobuild English Dictionary at hand, none of them carries the word, “unlevel,” much less “unleveler.”

Only Readers English Japanese Dictionary 2nd edition published by Japanese English dictionary specialist publisher carries ‘unlevel,’ which is defined as a. not flat. vt. make sth uneven.

Is “unlevel (unleveler)” an uncommon word, though I think its meaning is obvious?

P.S.

I checked Google Ngram Viewer which gives incidence rate in 2008:

level: 0.02636579705%

unlevel: 0.0000015076%

uneven: 0.0004579210%

Apparently, ‘unlevel’ seems to be uncommon word.

Answer 1

“unlevel (unleveler)” is an uncommon word, though its meaning is obvious.

Education then, beyond all other devices of human origin, is the great equalizer of the conditions of men, the balance-wheel of the social machinery. - Horace Mann, American education reformist (1796 – 1859)

"Unequalizer" didn't appeal to her, I guess (though she does use it in the body).

It also reflects the very common the great leveller/equalizer (death).

...we fat all creatures else to fat us, and we fat ourselves for maggots: your fat king and your lean beggar is but variable service, two dishes, but to one table: that's the end. - Hamlet.

and

"Our courts have their faults, as does any human institution, but in this country our courts are the great levelers, and in our courts all men are created equal." - Atticus Finch, To Kill a Mockingbird (Harper Lee)