Audra P. answered 02/22/19
State Champion Public Speaker and High School Speech Team Coach
Generally, I wouldn't.
Context is always important - so, it may depend on the subject/type of essay you're writing. For example, someone publishing the results of an scientific study often includes subheadings throughout, guiding the reader through their findings.
But as I assume we're referring to typical, classroom essay, you should be able to accomplish anything your "headings" would have, using good transitions and clear sentence structure.
Lets say we're talking about apples. In paragraph 3, we detailed the opinions of Apple expert Jeff who likes red apples best because they are ripe and sweet.
In the next paragraph we would like to point out how red apples are not the only ripe and sweet apple variety. So instead of inserting the heading "Other Ripe and Sweet Apples" above paragraph 4, we could just start the paragraph by saying, "Of course, the same could be said of other apple varieties. For instance..."
Does that make sense?
Great essays encourage the reader to keep reading. The natural rhythm of transitional phrases and clear ideas make readers want to know what's next. I believe subheadings make it very difficult to maintain any rhythm/flow in your essay.