Yet great, in our demotic culture, carries another meaning: it means "celebrated," and celebration is often the result of telling people, intentionally or not, what they wish to hear. Good writers can do this as well as bad writers.
Being considered a great writer in this sense is a political achievement, like winning the presidency. It's a symbiosis that has to do with the writer's times and the writer's relation to those times. How does the writer see the times, and how is he or she seen by them? What if the relationship is adversarial? What happens if the writer is inclined to commit the unpardonable sin of telling the truth? Does the Library of America take these factors into account?
Long ago I noticed, and I continue to notice, that the animus at the heart of most unfavorable comment about fiction is You didn't write the book I wanted you to! I am a disappointed consumer in a land where the customer is always right! Much favorable comment merely inverts this proposition; such noise is idiotic but at least doesn't hurt the writer's feelings. (Imaginative writers bruise easily, like peaches.) Lost in this welter of vainglory and petulance is the patient attempt to understand what was attempted, measure what was achieved, and describe the gap between the two. Some dare call this criticism, and while criticism might lack the autoerotic thrill of anointing the great or carrying out drive-by shootings on literary misfits, it remains our only trustworthy method of separating the good from the rest.