Do not you think by using simple sentences the essay would not be up to the mark. I am not not suggesting the use complex sentences entirely. But i think complex sentences add more maturity and style to your writing. As simple sentences are more commonly used and give your essay a mediocre look. While essay writing is not just the test of grammar and ideas, I think it also assess your style, which provides an insight to your command on language.

This is my views, please feel free to comment.